College Algebra Essentials WS 1 - FGCUfaculty.fgcu.edu/mnavarat/MAC1105/WS-bundle.pdfCollege Algebra...

College Algebra Essentials WS 1.5

Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the equation by factoring.

1) 7 - 7x = (4x + 9)(x - 1)

A) 1 B) {-4, 1} C) {-1, 4} D) 1, - 9

4

1)

Solve the equation by the square root property.

2) (x - 6)2 = -5

A) {-6 ± 5i} B) {1, 11} C) {6 ± i 5} D) {6 ± 5}

2)

Solve the equation by completing the square.

3) x2 + 4x - 9 = 0

A) {-2 - 13 , -2 + 13} B) {-1 - 13 , -1 + 13}

C) {2 + 13} D) {-2 - 1 13 , -2 + 1 13}

3)

Solve the equation using the quadratic formula.

4) 6x2 = -12x - 4

A)-3 - 15

3 , -3 + 15

3B)

-3 - 3

3 , -3 + 3

3

C)-12 - 3

3 , -12 + 3

3D)

-3 - 3

12 , -3 + 3

12

4)

Compute the discriminant. Then determine the number and type of solutions for the given equation.

5) x2 + 4x + 3 = 0

A) -28; two complex imaginary solutions

B) 4; two unequal real solutions

C) 0; one real solution

5)

Solve the problem.

6) A ladder that is 17 feet long is 8 feet from the base of a wall. How far up the wall does the ladder

reach?

A) 15 ft B) 3 ft C) 353 ft D) 225 ft

6)

1

College Algebra Essentials WS1.7

Name___________________________________


Use graphs to find the set.

1) (-∞, 3) ∪ [-9, 15)

A) (3, 15) B) [-9, 3) C) (-∞, -9] D) (-∞, 15)

1)

Solve the linear inequality. Other than ∅, use interval notation to express the solution set and graph the solution set on a

number line.

2) 4(x + 7) ≥ 3(x - 6) + x

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

A) (-∞, 3]

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

B) (-∞, ∞)

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

C) ∅

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

D) [3, ∞)

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

2)

Solve the compound inequality. Other than ∅, use interval notation to express the solution set and graph the solution set

on a number line.

3) -17 ≤ -2x - 3 < -11

A) (4, 7]

-1 0 1 2 3 4 5 6 7 8 9 10 11 12-1 0 1 2 3 4 5 6 7 8 9 10 11 12

B) (-7, -4]

-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1

C) [-7, -4)

-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1

D) [4, 7)

-1 0 1 2 3 4 5 6 7 8 9 10 11 12-1 0 1 2 3 4 5 6 7 8 9 10 11 12

3)

1

Solve the absolute value inequality. Other than ∅, use interval notation to express the solution set and graph the solution

set on a number line.

4) |x + 2| + 6 ≤ 11

A) (-7, 3)

-12 -10 -8 -6 -4 -2 0 2 4 6 8-12 -10 -8 -6 -4 -2 0 2 4 6 8

B) [-7, 3]

-12 -10 -8 -6 -4 -2 0 2 4 6 8-12 -10 -8 -6 -4 -2 0 2 4 6 8

C) (-∞, -7] ∪ [3, ∞)

-12 -10 -8 -6 -4 -2 0 2 4 6 8-12 -10 -8 -6 -4 -2 0 2 4 6 8

D) [-7, 11]

-12 -10 -8 -6 -4 -2 0 2 4 6 8-12 -10 -8 -6 -4 -2 0 2 4 6 8

4)

2


Name___________________________________


Give the domain and range of the relation.

1) {(1, -2), (-3, -1), (-3, 0), (-2, 1), (6, 3)}

A) domain: {1, -2, -3, 6}; range: {-2, -1, 1, 3}

B) domain: {-2, -1, 1, 3}; range: {1, -2, -3, 6}

C) domain: {-2, -1, 0, 1, 3}; range: {1, -2, -3, 6}

D) domain: {1, -2, -3, 6}; range: {-2, -1, 0, 1, 3}

1)

Determine whether the relation is a function.

2) {(-7, -1), (-7, 2), (-1, 8), (3, 3), (10, -7)}

A) Not a function B) Function

2)

Determine whether the equation defines y as a function of x.

3) x2 + y2 = 1

A) y is a function of x B) y is not a function of x

3)

4) y = 4x + 3

A) y is a function of x B) y is not a function of x

4)

Evaluate the function at the given value of the independent variable and simplify.

5) f(x) = 4x2 + 5x - 6; f(x - 1)

A) 4x2 - 3x + 3 B) 4x2 - 19x + 3 C) 4x2 - 3x - 7 D) -3x2 + 4x - 7

5)

Graph the given functions on the same rectangular coordinate system. Describe how the graph of g is related to the graph

of f.

6) f(x) = x , g(x) = x + 3

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

6)

1

A) g shifts the graph of f vertically up 3 units

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

B) g shifts the graph of f vertically down 3 units

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

C) g shifts the graph of f vertically down 3 units

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

2

D) g shifts the graph of f vertically up 3 units

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

Use the vertical line test to determine whether or not the graph is a graph in which y is a function of x.

7)

x

y

x

y

A) function B) not a function

7)

Use the graph to find the indicated function value.

8) y = f(x). Find f(3).

x-5 -4 -3 -2 -1 1 2 3 4 5

y5

4

3

2

1

-1

-2

-3

-4

-5

x-5 -4 -3 -2 -1 1 2 3 4 5

y5

4

3

2

1

-1

-2

-3

-4

-5

A) -3 B) 9 C) 3 D) 1.5

8)

3

Use the graph to determine the function's domain and range.

9)

x-10 -8 -6 -4 -2 2 4 6 8

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8

y10

8

6

4

2

-2

-4

-6

-8

-10

A) domain: [3, 4]

range: (-∞, ∞)

B) domain: (-∞, ∞)

range: [3, 4]

C) domain: [0, 4]

range: (-∞, ∞)

D) domain: (-∞, ∞)

range: [0, 4]

9)

Identify the intercepts.

10)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

A) (0, -4) B) (4, 0), (-4, 0)

C) (4, 0), (-4, 0), (0, 0) D) (4, 0), (-4, 0), (0, -4)

10)

4


Name___________________________________


Identify the intervals where the function is changing as requested.

1) Constant

x-5 -4 -3 -2 -1 1 2 3 4 5

y5

4

3

2

1

-1

-2

-3

-4

-5

x-5 -4 -3 -2 -1 1 2 3 4 5

y5

4

3

2

1

-1

-2

-3

-4

-5

A) (3, ∞) B) (-∞, -1) or (3, ∞)

C) (-∞, 0) D) (-1, 0)

1)

2) Increasing

x-5 -4 -3 -2 -1 1 2 3 4 5

y5

4

3

2

1

-1

-2

-3

-4

-5

x-5 -4 -3 -2 -1 1 2 3 4 5

y5

4

3

2

1

-1

-2

-3

-4

-5

A) (-2, 1) B) (-1, 3) C) (-1, ∞) D) (-2, -1) or (3, ∞)

2)

1

Use the graph of the given function to find any relative maxima and relative minima.

3) f(x) = x3 - 12x + 2

x-5 -4 -3 -2 -1 1 2 3 4 5

y20

16

12

8

4

-4

-8

-12

-16

-20

x-5 -4 -3 -2 -1 1 2 3 4 5

y20

16

12

8

4

-4

-8

-12

-16

-20

A) minimum: (2, -14); maximum: (-2, 18)

B) maximum: (-2, 18) and (0, 0); minimum: (2, -14)

C) no maximum or minimum

D) maximum: (2, -14); minimum: (-2, 18)

3)

Use possible symmetry to determine whether the graph is the graph of an even function, an odd function, or a function

that is neither even nor odd.

4)

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

A) Even B) Neither C) Odd

4)

2

5)

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

A) Even B) Odd C) Neither

5)

Graph the function.

6) f(x) = x + 1 if x < 1

4 if x ≥ 1

x-5 5

y

5

-5

x-5 5

y

5

-5

A)

x-5 5

y

5

-5

(1, 2)

(1, 4)

x-5 5

y

5

-5

(1, 2)

(1, 4)

B)

x-5 5

y

5

-5

(-1, 4)(-1, 2)

x-5 5

y

5

-5

(-1, 4)(-1, 2)

6)

3

C)

x-5 5

y

5

-5

(-1, 4)

(-1, 2)

x-5 5

y

5

-5

(-1, 4)

(-1, 2)

D)

x-5 5

y

5

-5

(1, 4)

(1, 2)

x-5 5

y

5

-5

(1, 4)

(1, 2)

Solve the problem.

7) Suppose a car rental company charges $102 for the first day and $52 for each additional or partial

day. Let S(x) represent the cost of renting a car for x days. Find the value of S(3.5).

A) $284 B) $232 C) $182 D) $258

7)

Find and simplify the difference quotient f(x + h) - f(x)

h, h≠ 0 for the given function.

8) f(x) = 1

6x

A)-1

x (x + h)B) 0 C)

1

6xD)

-1

6x (x + h)

8)

4


Name___________________________________


Use the given conditions to write an equation for the line in slope-intercept form.

1) Slope = -4, passing through (8, 4)

A) y = -4x + 36 B) y - 4 = x - 8 C) y - 4 = -4x - 8 D) y = -4x - 36

1)

2) Slope = 3

4, y-intercept = 2

A) f(x) = 3

4x + 2 B) f(x) = -

3

4x - 2 C) f(x) =

4

3x +

8

3D) f(x) =

3

4x - 2

2)

3) Passing through (4, 8) and (7, 3)

A) y = 5

3x +

44

3B) y = -

5

3x +

44

3

C) y - 8 = - 5

3(x - 4) D) y = mx +

44

3

3)

Graph the line whose equation is given.

4) y = 3

5x + 1

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

A)

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

B)

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

4)

1

C)

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

D)

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

Graph the equation in the rectangular coordinate system.

5) f(x) = -3

x-5 -4 -3 -2 -1 1 2 3 4 5

y5

4

3

2

1

-1

-2

-3

-4

-5

x-5 -4 -3 -2 -1 1 2 3 4 5

y5

4

3

2

1

-1

-2

-3

-4

-5

A)

x-5 -4 -3 -2 -1 1 2 3 4 5

y5

4

3

2

1

-1

-2

-3

-4

-5

x-5 -4 -3 -2 -1 1 2 3 4 5

y5

4

3

2

1

-1

-2

-3

-4

-5

B)

x-5 -4 -3 -2 -1 1 2 3 4 5

y5

4

3

2

1

-1

-2

-3

-4

-5

x-5 -4 -3 -2 -1 1 2 3 4 5

y5

4

3

2

1

-1

-2

-3

-4

-5

5)

2

C)

x-5 -4 -3 -2 -1 1 2 3 4 5

y5

4

3

2

1

-1

-2

-3

-4

-5

x-5 -4 -3 -2 -1 1 2 3 4 5

y5

4

3

2

1

-1

-2

-3

-4

-5

D)

x-5 -4 -3 -2 -1 1 2 3 4 5

y5

4

3

2

1

-1

-2

-3

-4

-5

x-5 -4 -3 -2 -1 1 2 3 4 5

y5

4

3

2

1

-1

-2

-3

-4

-5

6) 3y = 3

x-5 -4 -3 -2 -1 1 2 3 4 5

y5

4

3

2

1

-1

-2

-3

-4

-5

x-5 -4 -3 -2 -1 1 2 3 4 5

y5

4

3

2

1

-1

-2

-3

-4

-5

A)

x-5 -4 -3 -2 -1 1 2 3 4 5

y5

4

3

2

1

-1

-2

-3

-4

-5

x-5 -4 -3 -2 -1 1 2 3 4 5

y5

4

3

2

1

-1

-2

-3

-4

-5

B)

x-5 -4 -3 -2 -1 1 2 3 4 5

y5

4

3

2

1

-1

-2

-3

-4

-5

x-5 -4 -3 -2 -1 1 2 3 4 5

y5

4

3

2

1

-1

-2

-3

-4

-5

6)

3

C)

x-5 -4 -3 -2 -1 1 2 3 4 5

y5

4

3

2

1

-1

-2

-3

-4

-5

x-5 -4 -3 -2 -1 1 2 3 4 5

y5

4

3

2

1

-1

-2

-3

-4

-5

D)

x-5 -4 -3 -2 -1 1 2 3 4 5

y5

4

3

2

1

-1

-2

-3

-4

-5

x-5 -4 -3 -2 -1 1 2 3 4 5

y5

4

3

2

1

-1

-2

-3

-4

-5

Determine the slope and the y-intercept of the graph of the equation.

7) 6x + y + 11 = 0

A) m = - 1

6; 0, -

11

6B) m = -6; (0, -11)

C) m = 6; (0, -11) D) m = - 6

11; 0, -

1

11

7)

Graph the linear function by plotting the x- and y-intercepts.

8)1

3x + y - 2 = 0

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

A) intercepts: (0, 2), (6, 0)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

B) intercepts: (0, -6), (6, 0)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

8)

4

C) intercepts: (0, 2), (-2, 0)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

D) intercepts: (0, 2), (-6, 0)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

5


Name___________________________________


Find the average rate of change of the function from x1 to x2.

1) f(x) = -3x2 - x from x1 = 5 to x2 = 6

A)1

2B) -34 C) -2 D) -

1

6

1)

Find an equation for the line with the given properties.

2) The solid line L contains the point (3, 2) and is parallel to the dotted line whose equation is y = 2x.

Give the equation for the line L in slope-intercept form.

x-5 5

y

5

-5

x-5 5

y

5

-5

A) y = 2x - 4 B) y - 2 = 2(x - 3) C) y = 2x - 1 D) y = 2x + b

2)

Use the given conditions to write an equation for the line in the indicated form.

3) Passing through (2, 3) and parallel to the line whose equation is y = -2x + 3 ;

point-slope form

A) y - 3 = x - 2 B) y - 3 = -2(x - 2) C) y = 2x D) y - 2 = -2(x - 3)

3)

4) Passing through (2, 5) and perpendicular to the line whose equation is y = 1

6x + 8;

slope-intercept form

A) y = - 1

6x -

17

6B) y = - 6x - 17 C) y = - 6x + 17 D) y = 6x - 17

4)

1


Name___________________________________


Use the shape of the graph to name the function.

1)

x

y

x

y

A) Constant function B) Standard cubic function

C) Square root function D) Standard quadratic function

1)

2)

x

y

x

y

A) Identity function B) Standard cubic function

C) Absolute value function D) Constant function

2)

1

Use the graph of the function f, plotted with a solid line, to sketch the graph of the given function g.

3) g(x) = f(x - 1)

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

y = f(x)

A)

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

B)

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

C)

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

D)

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

3)

2

4) g(x) = - f(x) + 2

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

y = f(x)

A)

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

B)

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

C)

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

D)

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

4)

3

Begin by graphing the standard quadratic function f(x) = x2 . Then use transformations of this graph to graph the given

function.

5) g(x) = 2x2

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

A)

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

B)

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

C)

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

D)

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

5)

Use the graph of y = f(x) to graph the given function g.

4

6) g(x) = -2f(x)

x-12 -10 -8 -6 -4 -2 2 4 6 8 10 12

y12

10

8

6

4

2

-2

-4

-6

-8

-10

-12

x-12 -10 -8 -6 -4 -2 2 4 6 8 10 12

y12

10

8

6

4

2

-2

-4

-6

-8

-10

-12

A)

x-12 -10 -8 -6 -4 -2 2 4 6 8 10 12

y14

12

10

8

6

4

2

-2

-4

-6

-8

-10

-12

-14

x-12 -10 -8 -6 -4 -2 2 4 6 8 10 12

y14

12

10

8

6

4

2

-2

-4

-6

-8

-10

-12

-14

B)

x-12 -10 -8 -6 -4 -2 2 4 6 8 10 12

y14

12

10

8

6

4

2

-2

-4

-6

-8

-10

-12

-14

x-12 -10 -8 -6 -4 -2 2 4 6 8 10 12

y14

12

10

8

6

4

2

-2

-4

-6

-8

-10

-12

-14

C)

x-12 -10 -8 -6 -4 -2 2 4 6 8 10 12

y14

12

10

8

6

4

2

-2

-4

-6

-8

-10

-12

-14

x-12 -10 -8 -6 -4 -2 2 4 6 8 10 12

y14

12

10

8

6

4

2

-2

-4

-6

-8

-10

-12

-14

D)

x-12 -10 -8 -6 -4 -2 2 4 6 8 10 12

y14

12

10

8

6

4

2

-2

-4

-6

-8

-10

-12

-14

x-12 -10 -8 -6 -4 -2 2 4 6 8 10 12

y14

12

10

8

6

4

2

-2

-4

-6

-8

-10

-12

-14

6)

5

Begin by graphing the standard quadratic function f(x) = x2 . Then use transformations of this graph to graph the given

function.

7) h(x) = (1

2x + 2)

2

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

A)

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

B)

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

C)

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

D)

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

7)

6

Begin by graphing the standard function f(x) = x3 Then use transformations of this graph to graph the given function.

8) h(x) = 1

2(-2x)3

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

A)

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

B)

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

C)

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

D)

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

8)

7

Begin by graphing the standard square root function f(x) = x . Then use transformations of this graph to graph the given

function.

9) g(x) = - x + 1 - 1

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

A)

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

B)

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

C)

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

D)

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

9)

8

Begin by graphing the standard absolute value function f(x) = x . Then use transformations of this graph to graph the

given function.

10) g(x) = 1

2x + 4 + 6

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

A)

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

B)

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

C)

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

D)

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

10)

9

Use the graph of the function f, plotted with a solid line, to sketch the graph of the given function g.

11) g(x) = f(x - 2) - 2

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

y = f(x)

A)

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

B)

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

C)

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

D)

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

11)

10


Name___________________________________


Find the domain of the function.

1) f(x) = 10 - x

A) (-∞, 10) ∪ (10, ∞) B) (-∞, 10]

C) (-∞, 10] D) (-∞, 10) ∪ ( 10, ∞)

1)

2) f(x) = 5x

x + 7

A) (-∞, ∞) B) (-∞, -7) ∪ (-7, ∞)

C) (-∞, -7) D) (-∞, 0) ∪ (0, ∞)

2)

Given functions f and g, perform the indicated operations.

3) f(x) = 2x - 6, g(x) = 9x - 8

Find f - g.

A) 11x - 14 B) -7x - 14 C) -7x + 2 D) 7x - 2

3)

Given functions f and g, determine the domain of f + g.

4) f(x) = 2x - 1, g(x) = 2

x - 9

A) (-∞, -2) or (-2, ∞) B) (-∞, 9) or (9, ∞)

C) (0, ∞) D) (-∞, ∞)

4)

Find the domain of the indicated combined function.

5) Find the domain of (fg)(x) when f(x) = 6x + 2 and g(x) = 9x - 2.

A) Domain: 2

9, ∞ B) Domain: [0, ∞)

C) Domain: - 2

9, ∞ D) Domain: (-∞, ∞)

5)

For the given functions f and g , find the indicated composition.

6) f(x) = x2 + 2x + 2, g(x) = x2 - 2x - 3

(f∘g)(-3)

A) 17 B) 51 C) 170 D) 136

6)

Find the domain of the composite function f∘g.

7) f(x) = 2

x + 9, g(x) = x + 5

A) (-∞, -14) or (-14, ∞) B) (-∞, ∞)

C) (-∞, -9) or (-9, -5) or (-5, ∞) D) (-∞, -9) or (-9, ∞)

7)

8) f(x) = x; g(x) = 5x + 20

A) [-4, ∞) B) (-∞, ∞)

C) (-∞, -4] or [0, ∞) D) [0, ∞)

8)

1

Find functions f and g so that h(x) = (f ∘ g)(x).

9) h(x) = |4x + 6|

A) f(x) = |x|, g(x) = 4x + 6 B) f(x) = |-x|, g(x) = 4x - 6

C) f(x) = -|x|, g(x) = 4x + 6 D) f(x) = x, g(x) = 4x + 6

9)

2


Name___________________________________


Determine which two functions are inverses of each other.

1) f(x) = x - 2

3g(x) = 3x - 2 h(x) =

x + 2

3

A) None B) g(x) and h(x) C) f(x) and g(x) D) f(x) and h(x)

1)

Find the inverse of the one-to-one function.

2) f(x) = 6x - 7

5

A) f-1(x) = 5x + 7

6B) f-1(x) =

5

6x - 7C) f-1(x) =

5

6x + 7D) f-1(x) =

5x - 7

6

2)

3) f(x) = (x + 6)3

A) f-1(x) = 3

x - 216 B) f-1(x) = x - 6

C) f-1(x) = 3

x - 6 D) f-1(x) = 3

x + 6

3)

Does the graph represent a function that has an inverse function?

4)

x

y

x

y

A) No B) Yes

4)

1

5)

x

y

x

y

A) No B) Yes

5)

Use the graph of f to draw the graph of its inverse function.

6)

x-10 10

y

10

-10

x-10 10

y

10

-10

A)

x-10 10

y

10

-10

x-10 10

y

10

-10

B)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

6)

2

C)

x-10 10

y

10

-10

x-10 10

y

10

-10

D)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

Graph f as a solid line and f-1 as a dashed line in the same rectangular coordinate space. Use interval notation to give the

domain and range of f and f-1.

7) f(x) = x2 - 3, x ≥ 0

x-10 -8 -6 -4 -2 2 4 6 8

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8

y10

8

6

4

2

-2

-4

-6

-8

-10

A)

x-10 -8 -6 -4 -2 2 4 6 8

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8

y10

8

6

4

2

-2

-4

-6

-8

-10

f domain = (-∞, ∞); range = (-3, ∞)

f-1 domain = (-∞, ∞); range = (3, ∞)

B)

x-10 -8 -6 -4 -2 2 4 6 8

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8

y10

8

6

4

2

-2

-4

-6

-8

-10

f domain = (0, ∞); range = (-3, ∞)

f-1 domain = (0, ∞); range = (3, ∞)

7)

3

C)

x-10 -8 -6 -4 -2 2 4 6 8

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8

y10

8

6

4

2

-2

-4

-6

-8

-10

f domain = (0, ∞); range = (-3, ∞)

f-1 domain = (0, ∞); range = (-3, ∞)

D)

x-10 -8 -6 -4 -2 2 4 6 8

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8

y10

8

6

4

2

-2

-4

-6

-8

-10

f domain = (-∞, ∞); range = (-3, ∞)

f-1 domain = (-∞, ∞); range = (-3, ∞)

4


Name___________________________________


Find the distance between the pair of points.

1) (2, -1) and (6, -3)

A) 12 B) 12 3 C) 2 5 D) 6

1)

Find the midpoint of the line segment whose end points are given.

2) (- 8

3,

8

3) and (- 2, 1)

A) (- 14

3,

11

3) B) (-

1

3,

5

6) C) (

1

3, -

5

6) D) (-

7

3,

11

6)

2)

Write the standard form of the equation of the circle with the given center and radius.

3) (-3, 1); 7

A) (x - 3)2 + (y + 1)2 = 7 B) (x + 1)2 + (y - 3)2 = 49

C) (x + 3)2 + (y - 1)2 = 7 D) (x - 1)2 + (y + 3)2 = 49

3)

Graph the equation.

4) (x - 1)2 + (y - 2)2 = 49

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

A)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

Domain = (-8, 6), Range = (-9, 5)

B)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

Domain = (-6, 8), Range = (-5, 9)

4)

1

Complete the square and write the equation in standard form. Then give the center and radius of the circle.

5) x2 + y2 + 16x - 2y = -29

A) (x + 8)2 + (y - 1)2 = 36

(-8, 1), r = 6

B) (x - 1)2 + (y + 8)2 = 36

(-1, 8), r = 36

C) (x + 8)2 + (y - 1)2 = 36

(8, -1), r = 36

D) (x - 1)2 + (y + 8)2 = 36

(1, -8), r = 6

5)

Graph the equation.

6) x2 + y2 - 4x - 12y + 36 = 0

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

A)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

B)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

6)

2


Name___________________________________


The graph of a quadratic function is given. Determine the function's equation.

1)

x-10 -8 -6 -4 -2 2 4 6 8 10

y

10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8 10

y

10

8

6

4

2

-2

-4

-6

-8

-10

A) f(x) = x2 - 4x + 4 B) g(x) = x2 + 4x + 4

C) j(x) = x2 + 2 D) h(x) = x2 - 2

1)

Find the coordinates of the vertex for the parabola defined by the given quadratic function.

2) f(x) = (x + 4)2 + 7

A) (7, -16) B) (7, -4) C) (-4, 7) D) (-7, 4)

2)

Find the axis of symmetry of the parabola defined by the given quadratic function.

3) f(x) = (x + 4)2 - 6

A) x = 4 B) x = -4 C) x = -6 D) x = 6

3)

Find the range of the quadratic function.

4) f(x) = -7(x - 4)2 - 6

A) [-6, ∞) B) (-∞, 4] C) (-∞, -6] D) [-4, ∞)

4)

Find the x-intercepts (if any) for the graph of the quadratic function.

5) f(x) = 6 + 5x + x2

A) (3, 0) and (-2, 0) B) (3, 0) and (2, 0)

C) (-3, 0) and (-2, 0) D) (-3, 0) and (2, 0)

5)

Find the domain and range of the quadratic function whose graph is described.

6) The minimum is 6 at x = 1.

A) Domain: (-∞, ∞)

Range: (-∞, 6]

B) Domain: (-∞, ∞)

Range: [6, ∞)

C) Domain: [1, ∞)

Range: [6, ∞)

D) Domain: (-∞, ∞)

Range: [1, ∞)

6)

Use the vertex and intercepts to sketch the graph of the quadratic function.

1

7) f(x) = - 6x + 5 + x2

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

A)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

B)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

C)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

D)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

7)

Determine whether the given quadratic function has a minimum value or maximum value. Then find the coordinates of

the minimum or maximum point.

8) f(x) = -x2 - 2x - 6

A) maximum; - 5, - 1 B) maximum; - 1, - 5

C) minimum; - 1, - 5 D) minimum; - 5, - 1

8)

Solve the problem.

9) You have 344 feet of fencing to enclose a rectangular region. What is the maximum area?

A) 7396 square feet B) 118,336 square feet

C) 29,584 square feet D) 7392 square feet

9)

2

10) A rectangular playground is to be fenced off and divided in two by another fence parallel to one

side of the playground. 24 feet of fencing is used. Find the dimensions of the playground that

maximize the total enclosed area.

A) 4 ft by 6 ft B) 2 ft by 9 ft C) 6 ft by 6 ft D) 3 ft by 6 ft

10)

3


Name___________________________________


Find the domain of the rational function.

1) f(x) = x + 8

x2 - 4

A) {x|x ≠ -2, x ≠ 2} B) {x|x ≠ 0, x ≠ 4}

C) all real numbers D) {x|x ≠ -2, x ≠ 2, x ≠ -8}

1)

Use the graph of the rational function shown to complete the statement.

2)

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

As x→2-, f(x)→ ?

A) -2 B) +∞ C) 0 D) -∞

2)

3)

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

As x→2+, f(x)→ ?

A) -∞ B) +∞ C) 0 D) 2

3)

Find the vertical asymptotes, if any, of the graph of the rational function.

4) f(x) = x

x2 + 4

A) x = -4, x = 4 B) x = 4

C) x = -4 D) no vertical asymptote

4)

1

5) h(x) = x + 4

x2 - 16

A) x = -4 B) x = 4

C) x = 4, x = -4 D) no vertical asymptote

5)

Find the horizontal asymptote, if any, of the graph of the rational function.

6) h(x) = 20x3

5x2 + 1

A) y = 0 B) y = 1

4

C) y = 4 D) no horizontal asymptote

6)

7) f(x) = -10x

2x3 + x2 + 1

A) y = -5 B) y = - 1

5

C) y = 0 D) no horizontal asymptote

7)

Use transformations of f(x) = 1

x or f(x) =

1

x2 to graph the rational function.

8) f(x) = 1

x + 2 + 2

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

A)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

B)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

8)

2

C)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

D)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

Graph the rational function.

9) f(x) = 3x

x2 - 9

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

A)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

B)

x-20 -10 10 20

y

20

10

-10

-20

x-20 -10 10 20

y

20

10

-10

-20

9)

3

C)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

D)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

10) f(x) = x - 2

x2 - x - 42

x-12 -10 -8 -6 -4 -2 2 4 6 8 10 12

y6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x-12 -10 -8 -6 -4 -2 2 4 6 8 10 12

y6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

A)

x-12 -10 -8 -6 -4 -2 2 4 6 8 10 12

y6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x-12 -10 -8 -6 -4 -2 2 4 6 8 10 12

y6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

B)

x-12 -10 -8 -6 -4 -2 2 4 6 8 10 12

y6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x-12 -10 -8 -6 -4 -2 2 4 6 8 10 12

y6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

10)

4

C)

x-12 -10 -8 -6 -4 -2 2 4 6 8 10 12

y6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x-12 -10 -8 -6 -4 -2 2 4 6 8 10 12

y6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

D)

x-12 -10 -8 -6 -4 -2 2 4 6 8 10 12

y6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x-12 -10 -8 -6 -4 -2 2 4 6 8 10 12

y6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

5


Name___________________________________


Approximate the number using a calculator. Round your answer to three decimal places.

1) 5-1.9

A) -9.500 B) 0.347 C) -24.761 D) 0.047

1)

Graph the function by making a table of coordinates.

2) f(x) = 1

4

x

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

A)

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

B)

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

C)

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

D)

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

2)

Graph the function.

1

3) Use the graph of f(x) = ex to obtain the graph of g(x) = ex + 2.

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

3)

2

4) Use the graph of f(x) = ex to obtain the graph of g(x) = e-x.

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

4)

Solve the problem.

5) The population in a particular country is growing at the rate of 2.1% per year. If 10,184,000 people

lived there in 1999, how many will there be in the year 2006? Use f(x) = y0e0.021t and round to the

nearest ten-thousand.

A) 11,800,000 B) 14,160,000 C) 12,980,000 D) 11,560,000

5)

3

Use the compound interest formulas A = P 1 + r

n

nt and A = Pert to solve.

6) Find the accumulated value of an investment of $1130 at 8% compounded annually for 14 years.

A) $3073.17 B) $2305.20 C) $2395.60 D) $3319.03

6)

4


Name___________________________________


Write the equation in its equivalent logarithmic form.

1) 62 = x

A) logx

6 = 2 B) log2

x = 6 C) log6

2 = x D) log6

x = 2

1)

2) b3 = 1331

A) logb 1331 = 3 B) logb 3 = 1331 C) log3 1331 = b D) log1331 b = 3

2)

Evaluate the expression without using a calculator.

3) log4

1

16

A)1

2B) 2 C) -2 D) 8

3)

4) 2log

218

A) 2 B) 20 C) 18 D) log2

18

4)

The graph of a logarithmic function is given. Select the function for the graph from the options.

5)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

A) f(x) = log5

x + 1 B) f(x) = log5

(x - 1)

C) f(x) = log5

(x + 1) D) f(x) = log5

x

5)

Graph the functions in the same rectangular coordinate system.

1

6) f(x) = 4x and g(x) =log4x

x-6 6

y6

-6

x-6 6

y6

-6

A)

x-6 6

y

6

-6

x-6 6

y

6

-6

B)

x-6 6

y6

-6

x-6 6

y6

-6

C)

x-6 6

y6

-6

x-6 6

y6

-6

D)

x-6 6

y6

-6

x-6 6

y6

-6

6)

2

Graph the function.

7) Use the graph of f(x) = ln x to obtain the graph of g(x) = 4 ln x.

x-5 5

y

5

-5

x-5 5

y

5

-5

A)

x-5 5

y

5

-5

x-5 5

y

5

-5

B)

x-5 5

y

5

-5

x-5 5

y

5

-5

C)

x-5 5

y

5

-5

x-5 5

y

5

-5

D)

x-5 5

y

5

-5

x-5 5

y

5

-5

7)

Find the domain of the logarithmic function.

8) f(x) = log7

(x - 6)

A) (-∞, 6) or (6, ∞) B) (-6, ∞) C) (6, ∞) D) (-∞, 0) or (0, ∞)

8)

9) f(x) = log x + 2

x - 3

A) (-∞, -2) B) (3, ∞) C) (-∞, -2) ∪ (3, ∞) D) (-2, 3)

9)

3

Evaluate or simplify the expression without using a calculator.

10) log 10,000

A) 4 B) 40 C)2

5D)

1

4

10)

11) log 105

A) log 5 B) 5 C) 10 D) 105

11)

12) 8 log 104.1

A) 3.28 B) 11.2879 C) 32.8 D) 328

12)

13) ln 7

e

A)1

7B) 7e C)

e

7D) 7

13)

Evaluate the expression without using a calculator.

14) eln 136

A) 136 B) ln 136 C) -136 D) e136

14)

4


Name___________________________________


Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate

logarithmic expressions without using a calculator.

1) ln 3

x

A) 3ln x B) 3ln x C)1

3ln x D) x ln 3

1)

2) log6

x3

y8

A) 3 log6

x - 8 log6

y B) 8 log6

y - 3 log6

x

C) 3 log6

x + 8 log6

y D)3

8log

6(x

y)

2)

3) log3

7x

10y

z2

A)1

7log

3x ·

1

10log

3y ÷ 2 log

3z B)

1

7log

3x +

1

10log

3y - 2 log

3z

C) 7 log3

x + 10 log3

y - 2 log3

z D)7

3log

3x +

10

3log

3y -

2

3log

3z

3)

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose

coefficient is 1. Where possible, evaluate logarithmic expressions.

4) 6 ln x - 1

4 ln y

A) ln x6

4y

B) ln x64

y C) ln x6y4 D) ln x6

y4

4)

5) log x + log 13

A) (log x)(log 13) B) log x

13C) log (x + 13) D) log 13x

5)

6) 4 log6 4 + 1

7 log6 (r - 8) -

1

2 log6 r

A) log6 4r - 32

14rB) log6

2

7

r - 8

rC) log6

256r - 8

14rD) log6

2567

r - 8

r

6)

Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places

7) log24

386

A) 0.5336 B) 1.8741 C) 3.9668 D) 1.2064

7)

1


Name___________________________________


Solve the equation by expressing each side as a power of the same base and then equating exponents.

1) 4(3x - 5) = 256

A) {128} B) {-3} C) {3} D)1

64

1)

Solve the exponential equation. Express the solution set in terms of natural logarithms.

2) 2 x + 8 = 5

A)ln 5

ln 2 - 8 B) {ln 5 - ln 2 - ln 8}

C)ln 2

ln 5 + ln 8 D)

ln 2

ln 5 + 8

2)

Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the

solution.

3) 3 x + 6 = 8

A) 1.31 B) -4.11 C) 6.53 D) -0.35

3)

Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic

expressions. Give the exact answer.

4) ln x + 2 = 7

A) {e14 - 2} B) {e7 - 2} C) {e14 + 2} D)e7

2 + 2

4)

5) log4

(x + 2) - log4

x = 2

A) {2

15} B) {

15

2} C) {4} D) {

1

8}

5)

6) log (4 + x) - log (x - 4) = log 3

A)3

2B) ∅ C) {-8} D) {8}

6)

7) log (x + 23) - log 3 = log (10x + 3)

A)14

29B)

66

7C) -

66

7D) -

14

29

7)

Solve the problem.

8) The function A = A0e-0.01386x models the amount in pounds of a particular radioactive material

stored in a concrete vault, where x is the number of years since the material was put into the vault.

If 500 pounds of the material are initially put into the vault, how many pounds will be left after 140

years?

A) 700 pounds B) 390 pounds C) 72 pounds D) 89 pounds

8)

1


Name___________________________________


Solve the system of equations by the substitution method.

1)

x + y = 3

y = -2x

A) {(-3, 6)} B) {(3, 6)} C) {(3, -6)} D) {(-3, -6)}

1)

Solve the system by the addition method.

2) 4x + 7y = -10

-4x - 11y = 18

A) {(-1, 2)} B) {(-1, -2)} C) {(1, -2)} D) ∅

2)

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many

solutions, using set notation to express their solution sets.

3) x + y = -8

x + y = 5

A) {(-8, 5)} B) {(0, -3)}

C) {(x, y) x + y = -8} D) ∅

3)

4) y = 11 - 3x

12x + 4y = 44

A) {(5, -4)} B) {(0, 11)}

C) {(x, y) 3x + y = 11} D) ∅

4)

5) 5y = 44 - 6x

2x = 68 - 5y

A) {(5, -16)} B) {(-6, 16)}

C) {(x, y) 6x + 5y = 44 } D) ∅

5)

6) 5x - 9y = 6

-15x + 27y = -12

A)5

3, - 3 B) {(3, 2)}

C) {(x, y)| 5x - 9y = 6} D) ∅

6)

1

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars.

Use the information in the figure to answer the question.

7) Fewer than how many binoculars must be produced and sold for the company to have a profit loss?

A) 2250 binoculars B) 2700 binoculars C) 1500 binoculars D) 750 binoculars

7)

Solve the problem.

8) Steve invests in a circus production. The cost includes an overhead of $84,000, plus production

costs of $2000 per performance. A sold-out performance brings in $8000. Determine the number of

sold-out performances, x, needed to break even.

A) 16 performances B) 15 performances

C) 7 performances D) 14 performances

8)

2


Name___________________________________


Solve the system by the substitution method.

1) x + y = 11

y = x2 - 10x + 25

A) {(-7, 18), (-2, 13)} B) {(5, 6)}

C) {(7, 4), (2, 9)} D) {(7, 18), (2, 9)}

1)

Solve the system by the addition method.

2) x2 - y2 = 9

16x2 + 9y2 = 144

A) {(0, 3), (0, -3)} B) {(3, 0), (-3, 0)} C) {(0, 4), (0, -4)} D) {(4, 0), (-4, 0)}

2)

3) 2x2 + y2 = 66

x2 + y2 = 41

A) {(4, 5), (-4, 5), (4, -5), (-4, -5)} B) {(4, 5), (-4, -5)}

C) {(5, 4), (-5, -4)} D) {(5, 4), (5, -4), (-5, 4), (-5, -4)}

3)

Let x represent one number and let y represent the other number. Use the given conditions to write a system of nonlinear

equations. Solve the system and find the numbers.

4) The sum of the squares of two numbers is 5. The sum of the two numbers is -1. Find the two

numbers.

A) -2 and -1; 1 and 2 B) -2 and 1; -1 and 2

C) -1 and 2 D) -2 and 1

4)

Solve the problem.

5) The area of a garden is 12,000 square feet, and the length of its diagonal is 170 feet. Find the

dimensions of the garden.

A) 8 feet by 1500 feet B) 800 feet by 15 feet

C) 80 feet by 150 feet D) 120 feet by 100 feet

5)

1


Name___________________________________


Graph the inequality.

1) x - y < -2

x-10 10

y

10

-10

x-10 10

y

10

-10

A)

x-10 10

y

10

-10

x-10 10

y

10

-10

B)

x-10 10

y

10

-10

x-10 10

y

10

-10

C)

x-10 10

y

10

-10

x-10 10

y

10

-10

D)

x-10 10

y

10

-10

x-10 10

y

10

-10

1)

1

2) -2x - 4y ≤ -8

x-10 10

y

10

-10

x-10 10

y

10

-10

A)

x-10 10

y

10

-10

x-10 10

y

10

-10

B)

x-10 10

y

10

-10

x-10 10

y

10

-10

C)

x-10 10

y

10

-10

x-10 10

y

10

-10

D)

x-10 10

y

10

-10

x-10 10

y

10

-10

2)

2

3) x2 + y2 > 4

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

A)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

B)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

C)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

D)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

3)

3

4) y > x2 + 1

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

A)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

B)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

C)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

D)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

4)

4

5) y ≤ x2 - 7

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

A)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

B)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

C)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

D)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

5)

Graph the solution set of the system of inequalities or indicate that the system has no solution.

6) x + 2y ≥ 2

x - y ≤ 0

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

6)

5

A)

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

B)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

7) x2 + y2 ≤ 36

y > 3x

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

7)

6

A)

x-10 -8 -6 -4 -2 2 4 6 8 10

y

10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8 10

y

10

8

6

4

2

-2

-4

-6

-8

-10

B)

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8 10

y10

8

6

4

2

-2

-4

-6

-8

-10

C)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

D)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

7


Name___________________________________


Solve the problem.

1) A steel company produces two types of machine dies, part A and part B. The company makes a

$2.00 profit on each part A that it produces and a $6.00 profit on each part B that it produces. Let

x = the number of part A produced in a week and y = the number of part B produced in a week.

Write the objective function that describes the total weekly profit.

A) z = 2x + 6y B) z = 8(x + y)

C) z = 6x + 2y D) z =2(x - 6) + 6(y - 2)

1)

2) A dietitian needs to purchase food for patients. She can purchase an ounce of chicken for $0.25 and

an ounce of potatoes for $0.02. The dietician is bound by the following constraints.

· Each ounce of chicken contains 13 grams of protein and 24 grams of carbohydrates.

· Each ounce of potatoes contains 5 grams of protein and 35 grams of carbohydrates.

· The minimum daily requirements for the patients under the dietitian's care are 45 grams of

protein and 58 grams of carbohydrates.

Let x = the number of ounces of chicken and y = the number of ounces of potatoes purchased per

patient. Write a system of inequalities that describes these constraints.

A)

13x + 24y ≥ 45

5x + 35y ≥ 58

B)

13x + 24x ≥ 45

5y + 35y ≥ 58

C)

13x + 5y ≥ 45

24x + 35y ≥ 58

D)

13x + 5y ≥ 58

24x + 35y ≥ 45

2)

Find the maximum or minimum value of the given objective function of a linear programming problem. The figure

illustrates the graph of feasible points.

3) Objective Function: z = -x - 9y

Find maximum.

A) maximum: -30 B) maximum: -47 C) maximum: -22 D) maximum: -38

3)

1

An objective function and a system of linear inequalities representing constraints are given. Graph the system of

inequalities representing the constraints. Find the value of the objective function at each corner of the graphed region.

Use these values to determine the maximum value of the objective function and the values of x and y for which the

maximum occurs.

4) Objective Function z = 3x + 5y

Constraints x ≥ 0

y ≥ 0

2x + y ≤ 15

x - 3y ≥ -3

A) Maximum 22.5; at (7.5, 0) B) Maximum 75; at (0, 15)

C) Maximum 33; at (6, 3) D) Maximum 38; at (6, 4)

4)

2

College Algebra Essentials WS 1 - FGCUfaculty.fgcu.edu/mnavarat/MAC1105/WS-bundle.pdfCollege Algebra...

Documents

Transcript of College Algebra Essentials WS 1 - FGCUfaculty.fgcu.edu/mnavarat/MAC1105/WS-bundle.pdfCollege Algebra...