Fullerton College – Math 40 (Math Lab can help). Exam 1 Reviewstaffon a treadmill going at a...

Fullerton College – Math 40 (Math Lab can help). Exam 1 Review

TOPICS You should be comfortable with the following terms:

compound inequalities, interval and set-builder notation, algebraic expression, algebraic equation, R, N,Z, parallel and perpendicular lines, slope, rate of change, functions, linear function, non-linear equations,linear equations, vertical line test, x-intercept, y-intercept, linear inequality, ordered pair, ordered triples,consistent, inconsistent, independent, dependent, slope-intercept form, point slope form.

CONTENT This exam will cover the material dicussed in Chapters 2 and 3.

FORMULAS You should have the following formulas memorized. No Calculators.

Simple Interest

i = prt

Compound Interest Formula

A = p

⇣1 +

r

n

⌘nt

Motion Formula

D = R · T

Slope

m =y2 � y1

x2 � x1

Point Slope Form

y � y0 = m(x� x0)

Perpendicular Slope

m1m2 = �1

PRACTICE PROBLEMS

1. (2.2) Simplify given that a = 1, b = 2, c = 3,

d = 4, m =1

2, n =

2

3, p =

1

4, and x = 0

(a)

pa+ c

2+

p6n

b

!÷ (c+ d)

pp

(b)b

2 � c

32ab�m

� n

b�m

2. (2.2) Given:1

f

=1

p1� 1

p2, solve for p2.

3. (2.3) At a going-out-of-business sale, furni-ture is selling at 40% o↵ the regular price. Inaddition, green-tagged items are reduced byan additional $20. If Alice Barr purchaseda green-tagged item and paid $136, find theitem’s regular price.

4. (2.3) At the Kansas City airport, the cost torent a Ford Focus from Hertz is $24.99 perday with unlimited mileage. The cost to rentthe same car from Avis is $19.99 per day plus$0.10 per mile that the car is driven. If Cathy

Panik needs to rent a car for 3 days, determinethe number of miles she would need to drivein order for the cost of the car rental to be thesame from both companies.

5. (2.4) Space Shuttle 2 takes o↵ 30 mins afterShuttle 1 takes o↵. If Shuttle 2 travels 300miles per hour faster than Shuttle 1 and over-takes Shuttle 1 exactly 5 hours after Shuttle 2takes o↵, find the speed of Shuttle 1.

6. (2.4) James Hetfield, the owner of a gourmetco↵ee shop, has two co↵ees, one selling for$6.00 per pound and the other for $6.80 perpound. How many pounds of each type of cof-fee should he mix to make 40 pounds of co↵eeto sell for $6.50 per pound?

7. (2.5) Patrice Lee’s first four exam scores are94, 73, 72, and 80. If a final average greaterthan or equal to 80 and less than 90 is neededto receive a final grade of B in the course, whatrange of scores on the fifth and last exam willresult in Patrice’s receiving a B in the course?Assume a maximum score of 100.

1


8. (2.5) Write the solution in interval notationand set-builder notation:

(a)x

2+

1

5> x� 2x

3+

1

6or

7� 2x

3 �5

(b)x

2+

1

5> x� 2x

3+

1

6and

7� 2x

3 �5

9. (2.6) Solve:

(a)3|1� 2x|+ 4

2= 1

(b)2

3+

2� 4

��1�2

3x

��2

= �1

10. (2.6) Solve:

��2x� 3

5+ 1

�� =��3x

4� 1

3

��

11. (3.2) Given the following relations, statewhether it is function or not, domain, andrange.

(a)

(b)

(c) { (-2, 0), (2, 1), (7, 0), (.5, 4)}

12. (3.3) The yearly profit, p, of a bagel com-pany can be estimated by the function p(x) =0.1x� 5000, where x is the number of bagelssold per year.

(a) Draw a graph of profits versus bagels soldfor up to and including 250,000 bagels.

(b) Estimate the number of bagels that mustbe sold for the company to break even.

(c) Estimate the number of bagels sold if thecompany has $22,000 profit.

(d) What does the y-intercept tell you aboutthe profit?

13. (3.4) If the slope of the following coordinates

(x, 2) and

✓�7,

1

3

◆is �3

5, find x.

14. (3.4) If the graph of y + 2x = 5 is translateddown 4 units, determine the equation of thetranslated graph.

15. (3.5) Find the equation of the line that passesthrough (4,3) and is perpendicular to the line

that goes through the coordinates

✓1

2,

1

3

◆and

✓1

4,

1

5

◆.

2


16. (3.5) Find the equation of the line that passesthough (0,4) and is parallel to the line that

goes through the coordinates

✓�1,

2

3

◆and

(5,�2).

17. (3.5) The number of calories burned for 1 houron a treadmill going at a constant speed is afunction of the incline of the treadmill. At 4miles per hour a person on a 5� incline willburn 525 calories. At 4 mph on a 15� inclinethe person will burn 880 calories. Let C be thecalories burned and d be the degrees of inclineof the treadmill. Determine a linear functionthat fits the data.

18. (3.6) Use the colorful graph below to answer(a) - (e).

(a) (f + g)(0) (b) (gh)(2) (c)

✓h

g

◆(0)

(d) (f � g)(2) (e) (f + g)(�2)� (h+ f)(1)

19. (3.7) Patrick Cunningham is taking somefriends and their families to the stock-car races.Tickets cost $8 for children and $15 for adultsand Patrick only has $175 to spend. Letx represent the number of children’s ticketspurchased and let y represent the number ofadults’ tickets purchased. Write a linear in-equality in which the total cost for the ticketsis less than or equal to $175.

(a) Determine if Patrick has enough money topurchase tickets for 10 children and 8 adults?

(b) Determine if Patrick has enough money topurchase tickets for 8 children and 6 adults?

3


Answers

1. (a)1

7(b)

26

63

2. p2 =p1f

f � p1

3. $260

4. 150 mi

5. 3,000 miles per hour (mi/hr)

6. 15 lbs - $6 and 25 lbs - $25

7. {x | 81 x 100}

8. (a) I.N.

✓�1

5,1◆, S.B.

⇢x|x > �1

5

�

(b) I.N. [11,1), S.B. {x|x � 11}

9. (a) { } (b)

⇢�1

2,

7

2

�

10.

⇢� 4

69,

44

21

�

11. (a) Function, D: [-2.5, 5], and R: [-2,2]

(b) Not a Function, D: [0,2], and R: [-2,2]

(c) Function, D:{-2, .5, 2, 7}, and R: {0, 1, 4}

12. (a)

(b) 50,000 bagels

(c) 270,000 bagels

(d) $5,000 loss in profit

13. x = �88

9

14. y = �2x+ 1

15. y = �15

8x+

21

2

16. y = �4

9x+ 4

17. C(d) = 35.5d+ 347.5

18. (a) (f + g)(0) = �3 (b) (gh)(2) = �1

(c)

✓h

g

◆(0) =

1

6(d) (f � g)(2) = 1

(e)(f + g)(�2)� (h+ f)(1) = 0

19. 8x+ 15y 175 (a) No (b) Yes

4



area of rectangle, area of a triangle, factor completely, system of linear equations, system of equations,synthetic division, remainder theorem, zero-factor property, polynomial, degree, term, coe�cient, systemof linear inequalities, system of inequalities

CONTENT This exam will cover the material dicussed in Sections 4.1 - 4.3, 4.6 and Chapter 5.


Di↵erence of squares

a

2 � b

2 = (a+ b)(a� b)

Sum and Di↵erence of Cubes

a

3 � b

3 = (a� b)(a2 + ab+ b

2)

a

3 + b

3 = (a+ b)(a2 � ab+ b

2)

PRACTICE PROBLEMS

1. (4.2) Solve the following systems of equations:

(a)

8>>>>>>><

>>>>>>>:

x� y + 2

5= z + 4

y � z + 4

2= x� 6

z � x� 7

3= y � 5

(b)

8>>>>>>><

>>>>>>>:

1

x

+1

y

= 5

1

x

+1

z

= 6

1

y

+1

z

= 7

2. (4.3) Set-up a system of linear equations andsolve

(a) Hassan Sa↵ari, an o�ce equipment sales rep-resentative, earns a weekly salary plus a com-mission on his sales. One week his total com-pensation on sales of $4000 was $660. The nextweek his total compensation on sales of $6000was $740. Find Hassan’s weekly salary and hiscommission rate.

(b) Pola Sommers, a massage therapist, needs 3ounces of a 20% lavender oil solution. She hasonly 5% and 30% lavender oil solutions available.

How many ounces of each should Pola mix toobtain the desired solution?

(c) Kapitan is a restaurant with 23 employees.The number of waiters is twice the number ofmanagers and there are three more chefs thanmanagers. Find the number of managers, wait-ers, and chefs.

(d) As of 2014, the states of Florida, Califor-nia, and Louisiana have hosted the most SuperBowls. These three states hosted a total of36 Super Bowls. Florida hosted 5 more SuperBowls than Louisiana. Together, Florida andLouisiana hosted three more than twice the num-ber California hosted. Determine the numberof Super Bowls hosted by each of these threestates.

3. (4.6) Determine the solutions to the followingsystems of inequalities:

(a)

8<

:�4x+ 5y < 20

x � �3(b)

(3x� y 4

3x� y > 4

(c)

(y � x

2

y 4(d)

8>>>>>>>>>><

>>>>>>>>>>:

x 4

x+ y 6

x+ 2y 8

x � 0

y � 0

4. (5.1) Subtract the the sum of a5 � 7a3x2 + 9, �20a4x+ 21a2x3 � 19ax4, and x

5 � 7ax4 + 9a3x2 � 80from the sum of �4x5 + 18a3x2 � 8, �9a4x� 17a3x2 + 11a2x3, and a

5 + 36.

1


5. (5.2) Multiply and simplify the following polynomials:

(I) (amb

n + 3am�1b

n+2 � a

m�2b

n+4 + a

m�3b

n+6)4amb

3

(II) (ma�1 +m

a+1 +m

a+2 �m

a)(m2 � 2m+ 3)

(III) [(m+ n)(m� n)� (m+ n)(m+ n)][2(m+ n)� 3(m� n)]

6. (5.1 - 5.3) Use the following polynomial functionbelow to solve for (a) - (c).

P (x) = x� x

2

(a) P (2) (b) P (�a)

(c)P (a+ h)� P (a)

h

7. (5.3) Divide by using Synthetic Division:

(a) (7x+ 12 + 8x3 � 6x2)÷ (4x+ 3)

(b)2x3 � x

2y � 7xy2 + 2y3

x� 2y

8. (5.3) Use the Remainder Theorem to determine:

(a) if x+ 2 is a factor of P (x) = x

3 � 7x� 6.

(b) G

✓2

3

◆for G(x) = 3x5 � 5x4 + x+ 1

9. (5.3) Find P (x) ifP (x)

x+ 4= x+ 5 +

6

x+ 4

10. (5.5 - 5.7) Factor completely the following (ifpossible):

(a) �4 + 15x4 � 17x2

(b) (m+ n)2 � 6(m+ n) + 9

(c) (a2 � 1)2 + 5(a2 � 1)� 24

(d) 4a2m+ 12a2n� 5bm� 15bn

(e) m4ax+ 8a4x4

m

11. (5.8) Solve for x:

(a) (x+ 4)2 = 2x(5x� 1)� 7(x� 2)

(b) x2 + xy + ax+ 3ay = �2ax

12. (5.8) The area of a triangle is 3 ft

2. The baseof the triangle is 2x while its height is 2x + 1,find the actual base and height of the trianglein ft.

13. (5.8) Two cyclists, Mark Molino and KrisMudunuri, start at the same point. Mark rideswest and Kris rides north. At some time, theyare 13 miles apart. If Mark traveled 7 miles far-ther than Kris, determine how far each persontraveled.

2


Answers

1. (a) (10, 8, 4) (b)

✓1

2,

1

3,

1

4

◆

2. (a) Let w = weekly salary and c = commission

rate

(4000c+ w = 660

6000c+ w = 740

$500 and 4%

(b) Let x = ounces of 5% lavender oil and

y = ounces of 30% lavender oil

(x+ y = 3

.05x+ .3y = 3(.2)

1.2 ounces of 5%, 1.8 ounces of 30%

(c) Let M = managers, W = waiters, and

C = chefs

8><

>:

M +W + C = 23

W = 2M

C = 3 +M

5 managers, 10 waiters, 8 chefs

(d) Let F = Florida, L = Louisiana, and

C = California

8><

>:

F + L+ C = 36

F = 5 + L

L+ F = 2C + 3

Florida: 15, California: 11, Louisiana: 10

3. (a)

(b) ;

(c)

(d)

4. 11a4x� a

3x

2 � 10a2x3 + 26ax4 � 5x5 + 99

5. (I) 4a2mb

n+3 + 12a2m�1b

n+5 � 4a2m�2b

n+7 +4a2m�3

b

n+9

(II) ma+4 �m

a+3 + 6ma+1 � 5ma + 3ma�1

(III) 2m2n� 8mn

2 � 10n3

6. (a)P (2) = �2 (b)P (�a) = �a� a

2

(c) 1� 2a� h

7. (a) 2x2 � 3x+ 4 (b) 2x2 + 3xy � y

2

8. (a) Yes (b) G

✓2

3

◆=

29

27

9. P (x) = x

2 + 9x+ 26

10. (a) (5x2 + 1)(3x2 � 4) (b) (m+ n� 3)2

(c) (a2 + 7)(a� 2)(a+ 2)

(d) (m+ 3n)(4a2 � 5b)

(e) amx(m+ 2ax)(m2 � 2amx+ 4a2x2)

11. (a) x = 2 or x = �1

9(b) x = �y or x = �3a

12. base: 2 ft, height: 3 ft

13. Kris: 5 miles, Mark: 12 miles

3



Rational expressions, rational functions, complex Fractions, proportions, similar figures, direct variation, inverse

variation, joint variation, radical equations, complex numbers (C), conjugates, completing the square, quadratic

formula, exponential rules, square root property

CONTENT This exam will cover the material discussed in Ch 6 - 7, and §8.1 - 8.2.


Direct Variation

y = kx

Inverse Varation

y =

k

x

Joint Varation

y = kxy

Quadratic Formula

x =

�b±

p

b

2� 4ac

2a

PRACTICE PROBLEMS

1. (6.1-2) Solve the following systems of equations:

(a)

(a

2� ax)

2

a

2+ x

2·

1

a

3+ a

2x

÷

✓a

3� a

2x

a

2+ 2ax+ x

2·

a

2� x

2

a

3+ ax

2

◆

(b)

(a

2� 3a)

2

9� a

2·

27� a

3

(a+ 3)

2� 3a

÷

a

4� 9a

2

(a

2+ 3a)

2

(c)

2

x� 2

+

2x+ 3

x

2+ 2x+ 4

�

6x+ 12

x

3� 8

(d)

3x+ 2

x

2+ 3x� 10

�

5x+ 1

x

2+ 4x� 5

+

4x� 1

x

2� 3x+ 2

(e) If the area of a rectangle is

x

2+ 11x+ 30

x+ 2

and the

length is

x

2+ 9x+ 18

x+ 3

, find the width.

2. (6.2) If f(x) =

x

x

2� 9

and g(x) =

x+ 4

x� 3

, find

(a) the domain of f(x).

(b) the domain of g(x).

(c) (f + g)(x).

(d) the domain of (f + g)(x).

3. (6.3) Set-up a system of linear equations and solve

(a)

a

a+ x

�

a

2a+ 2x

a

a� x

+

a

a+ x

(b)

m

2

n

�

m

2� n

2

m+ n

m� n

n

+

n

m

4. (6.4) Solve:

(a)

x� 3

x� 2

+

x+ 1

x+ 3

=

2x

2+ x+ 1

x

2+ x� 6

(b)

3

p+ 1

+

5

p+ 3

=

6

p

2+ 4p+ 3

(c)

x

x� 8

+

6

x� 2

=

x

2

x

2� 10x+ 16

5. (6.5) Mariano and Concepcion plan to plant a flower

garden. Together, they can plant a garden in 4.2 hours.

If Mariano by himself can plant the same garden in 6

hours, how long will it take Concepcion to plant the

garden by herself?

6. (6.6)

(a) W is directly proportional to the square of L and

inversely proportional to A. If W = 4 then L = 2 and

A = 10, find W then L = 5 and A = 20.

(b) z is jointly proportional to x and y and inversely

proportional to the square of r. If z = 120 when

x = 20, y = 8, and r = 8, find r when x = 10, y =

1

6

,

and z = 640.

7. (7.2)

(a) Write in exponential form:

(i)

3p

x

5(ii) (

4p

y)

5(iii)

4p

x

2yz

1


(b) Write in radical form:

(i) a

2/3(ii) (8m

2n)

7/4(iii) (x+ y)

�5/3

(c) Evaluate: 64�1/2+ 8

�2/3

8. (7.2 - 5) Simplify (assume all variables are positiveintegers ).

(a)

3p125x

8y

9z

16

(b)

3p2x

2y(

3p4x

4y

7+

3p

9x)

(c)

q3px

5y

2

(d)

✓�27y

2/5z

1/3

x

�1y

3/5

◆�2/3

(e)

4p48x

9y

3

4p

3xy

15

(f) (

p

3 + 2)

2

(g) Rationalize the denominator:

p

x

p

x+

p

y

(h)

p

2�

3

p

32

+

p

50

(i) 8

3px

7y

8�

3px

4y

2+ 3

3px

10y

2+

5pxy

2

(j)

3p(x+ y)

5

p(x+ y)

3

9. (7.6) Solve:

(a)

p

x+ 3 =

p

3x+ 9

(b)

p

3x+ 4 =

p

5x+ 14

(c)

p

6x� 5�

p

2x+ 6� 1 = 0

(d)

p6 +

p

x+ 4 =

p

2x� 1

10. (7.7) Perform the indicated operation:

(a) (

p

3 +

p

�5)� (11

p

3�

p

�7)

(b)

p

3

5�

p

�6

(c)

5

3i

(d) Evaluate: x2� 2x+ 9, x = 1 + 2i

p

2

(e) i

805

11. (8.1) Solve by using the Square Root Property:

(a) (5x+ 9)

2+ 4 = 0

(b)

✓3x�

1

4

◆2

=

9

25

12. (8.1) Complete the Square for the following:

(a) �x

2= 6x� 27

(b) 2z

2� 7z � 4 = 0

13. (8.2) Determine whether each equation has two dis-

tinct real solutions, single real solutions, or no real

solutions.

(a) 4x

2� 12x+ 9 = 0

(b) 5x

2� 2x+ 7 = 0

(c) 5p

2+ 3p� 7 = 0

14. (8.2) Solve:

(a) (14d+ 9)(d� 1) = �3

(b) h =

h� 6

4� h

2


Answers

1. (a)

1

a

(b) a

3� 3a

2= a

2(a� 3) (c)

4x+ 5

x

2+ 2x+ 4

(d)

2x

2+ 27x� 5

(x� 1)(x� 2)(x+ 5)

(e)

x+ 5

x+ 2

2. (a) {x|x 2 R and x 6= �3, 3}

(b) {x|x 2 R and x 6= 3}

(c)

x

2+ 8x+ 12

(x� 3)(x+ 3)

=

(x+ 6)(x+ 2)

(x� 3)(x+ 3)

(d) {x|x 2 R and x 6= �3, 3}

3. (a)

a� x

4a

(b) m

4. (a) x = �6, Restrictions: x 6= 2,�3

(b) No Solution, Restrictions: p 6= �3,�1

(c) x = 12, Restrictions: x 6= 2, 8

5. 14 hours

6. (a)W =

25

2

(b) r = ±

p

2

4

7. (a) (i) x

5/3(ii) y

5/4(iii) (x

2yz)

1/4

(b) (i)

3p

a

2(ii) (

4p

8m

2n)

7(iii)

1

(

3p

x+ y)

5

(c)

3

8

8. (a) 5x

2y

3z

5 3p

x

2z (b) 2x

2y

2 3py

2+ x

3p

18y

(c) x

5/6y

1/3(d)

y

2/15

9x

2/3z

2/9

(e)

2x

2

y

3(f) 7 + 4

p

3

(g)

p

x(

p

x�

p

y)

x� y

=

x�

p

xy

x� y

(h)

45

p

2

8

(i) (8x

2y

2� x+ 3x

3)

3p

xy

2+

5pxy

2

(i) (x+ y)

1/6=

6p

x+ y

9. (a) x = 0, 9 (b) x = �5 (c) x = 5 (d) x = 5

10. (a) �10

p

3 + (

p

5 +

p

7)i (b)

5

p

3

31

+

p

18

31

i

(c) �

5

3

i (d) 0 (e) i

11. (a) x = �

9

5

±

2

5

i (b) x =

17

60

,�

7

60

12. (a) x = 3,�9 (b) z = 4,�

1

2

13. (a) One Real Soln. (b) No Real Soln.

(c) Two Real Solns.

14. (a) d =

5±

p

361

28

(b) h =

3

2

±

p

33

2

, Restriction: h 6= 4

3



Quadratic in Form, vertex, axis of symmetry, parabola, translations, quadratic inequalities, rational inequalities,composite functions, one-to-one functions, vertical line test, horizontal line test, inverse functions, exponentialfunctions, logarithms, logarithmic functions, properties of logarithms (as well natural logarithms), natural exponentialfunction, compound interest, change of base, conics, distance formula, circle, radius, ellipse

CONTENT This exam will cover the material discussed §8.3 - 8.6, Ch 9, and §10.1 - 10.2.


Standard Form

f(x) = ax

2 + bx+ c

Vertex: V

✓�

b

2a, f

✓�

b

2a

◆◆

Axis of Symmetry: x = �

b

2a

Vertex Form

f(x) = a(x� h)2 + k

Vertex: V (h, k)

Axis of Symmetry: x = h

Exponential Form to Logarithmic Form (Vice Versa)

y = loga

x () a

y = x

y = lnx () e

y = x

Logarithmic Rules

loga

(pq) = loga

p + loga

q

loga

✓p

q

◆= log

a

p� loga

q

loga

(pr) = r loga

p

loga

a

r = r

a

loga m = m

loga

1 = 0

Change of Base

loga

x =log

b

x

logb

a

Distance Formula

d =p

(x2

� x

1

)2 + (y2

� y

1

)2

Midpoint Formula

M

✓x

1

+ x

2

2,

y

1

+ y

2

2

◆

Circle with center at (h,k)

(x� h)2 + (y � k)2 = r

2

Ellipse with center at (h,k)

(x� h)2

a

2

+(y � k)2

b

2

= 1

PRACTICE PROBLEMS

1. (8.3) (a) The larger of two positive numbers is 4 greaterthan the smaller. Find the two numbers if their prod-uct is 77.

(b) The distance, d, in feet, that an object is from theground t seconds after being dropped from an airplaneis given by the formula d = �16t2 + 784. (i) Find thedistance the object is from the ground 2 seconds afterit has been dropped. (ii) When will the object hit theground?

2. (8.4) Solve (Hint: Use u-substitution)

(a) x4

� 21x2 + 80 = 0.

(b) 6(x� 2)�2 = �13(x� 2)�1 + 8

(c) 2p2/3 � 7p1/3 + 6 = 0

(d) Find all x�intercepts of the given function.

(i) f(x) = x� 8p

x+ 12

(ii) f(x) = (x2

� 6x)2 � 5(x2

� 6x)� 24

3. (8.5) Josh Vincent tosses a ball upward from the topof a 75-foot building. The height, s(t), of the ballat any time t, in seconds, can be determined by thefunction s(t) = �16t2 + 80t+ 75.

1


(a) At what time will the ball attain its maximumheight?

(b) What is the maximum height?

4. (8.5) Find the vertex, axis of symmetry, x-intercepts,y-intercepts, and graph.

(a) f(x) = 2x2 + 4x+ 5

(b) g(x) = �x

2

� 5x� 4

5. (8.5) Covert to y = a(x� h)2 + k and find the vertex,axis of symmetry, and graph.

(a) k(x) = �2x2 + 16x� 31

(b) m(x) = 3x2 + 12x+ 11

6. (8.6) Solve each inequality and give the solution ininterval notation.

(a) 4x4

� 9x2

0

(b) 6x2

> 30

(c)2x

x� 2 1

(d)2x+ 3

3x� 5> 4

7. (9.1) Given that f(x) =p

1� x, g(x) = x � x

2, andh(x) = 4� 5x. Find the following:

(a) (f �g)(�3) (b) (h � g)(2) (c) (h � f)(x)

(d) (g � f)(x) (e) (f � g � h)(x)

8. (9.1) Determine if each of the following functions isone-to-one, if so, find the inverse.

(a) f(x) =4x� 3

5(b) g(x) = 3� x

2

(c) h(x) =p

1� x

9. (9.2) Graph:

(a) f(x) = 4x

(b) g(x) =

✓1

4

◆x

(c) h(x) = 5x�1 + 2

10. (9.3) Change the following from exponential form tologarithmic or vice versa.

(a) 82 = 16

(b) log2

32 = 5

(c) 4~ = �

(d) log~ ©= ß

11. (9.3) Graph:

(a) f(x) = log2

x (b) f(x) = log2

(x+ 1)

12. (9.4, 9.7) Use the properties of logarithms to expandor combine as a single expression.

(a) log4

r16

a+ 2(b) ln

e

2

x

3

y

z

p

w

(c) 2 ln(n+ 1)� 3 lnn�

1

2ln(n� 1)

(d) 1 + log9

4 + log9

(r � 6)� log9

(r2 � 36)

13. (9.4) Evaluate

(a) (23)log8 7 (b) 5( 4p

81)log3 5

(c)1

2log

6

3p

6 (d) log8

(log5

8p

5)

14. (9.5) Use a calculator to solve for the following prob-lems and round to four decimal places.

(a) 10�3.157

(b) log x = 4.063

(c) e2.3

(d) ln 5�1

15. (9.6 - 9.7) Solve (Give exact solutions)

(a)

✓1

27

◆x

· 243x+1 = 81x�1 (b) 8x+1 = 5

(c) 5x = 3x+2 (d) log9

(r + 2) = log9

(3r � 1)

(e) log7

(2x+ 9)� log7

(2x) = log7

✓1

2x+ 1

◆

(f) log2

y + log2

(y � 7) = 3

(g) ln(10x2

� 9x� 7)� ln(2x+ 1) = ln(7x+ 1)

(h) log x+ log(x� 3) = 1

2


16. (10.1)

(a) Convert to x = a(y � k)2 + h and Graph

x = 3y2 � 12y � 36

(b) Find the Distance and Midpoint of

✓�

1

4, 6

◆to

✓�

3

4, 6

◆.

(c) Find the center and radius of the circle given

x

2 + y

2 + 4x� 6y � 3 = 0

17. (10.2) Graph

(a) 49x2 + y

2 = 49

(b) 12(x+ 4)2 + 3(y � 1)2 = 48

3


Answers

1. (a) 7 and 11 (b) (i) 720 ft (ii) 7 seconds

2. (a) x = ±4 and x = ±

p

5

(b) x = 4,13

8

(c) p =27

8, 8

(d) (i) (36,0), (4,0) (ii) (3±p

17, 0), (3±p

6, 0)

3. (a)5

2seconds (b) 175 ft

4. (a) V (�1, 3), A.O.S.: x = �1, (0,5), No x-int.

(b) V

✓�

5

2,

9

4

◆, A.O.S.: x = �

5

2, (0,-4), (-4,0),

(-1,0)

5. (a) k(x) = �2(x� 4)2 + 1, V (4, 1), A.O.S.: x = 4

(b) m(x) = 3(x+2)2�1, V (�2,�1), A.O.S.: x = �2

6. (a)

�

3

2,

3

2

�(b) (�1,�

p

5) [ (p

5,1)

(c) [�2, 2) (d)

✓5

3,

23

10

◆

7. (a) (f � g)(�3) =p

13 (b) (h � g)(2) = 14

(c) (h � f)(x) = 4� 5p

1� x

(d) (g � f)(x) =p

1� x� 1 + x

(e) (f � g � h)(x) =p

13� 35x+ 25x2

8. (a) One-to one; f�1(x) =5x+ 3

4

(b) Not one-to-one.

(c) One-to-one; h�1(x) = 1� x

2; x � 0

4


9. (a)

(b)

(c)

10. (a) log8

16 = 2 (b) 25 = 32

(c) log4 � = ~ (d) ~ ß = ©

11. (a)

(b)

12. (a) 1�1

2log

4

(a+ 2)

(b) 2 + 3 lnx+ ln y � ln z �1

2lnw

(c) ln(n+ 1)2

n

3

p

n� 1(d) log

9

36

r + 6

13. (a) 7 (b) 25 (c)1

6(d) -1

14. (a) ⇡ .0007

(b) ⇡ 11, 561.1224

(c) ⇡ 9.9742

(d) ⇡ �1.6094

15. (a) x =9

2

(b) x = log8

5� 1 = log8

5� log8

8 = log5

5

8

(c) x =2

log3

5� 1= log

5/3

9

(d) r =3

2(e) x = 3 (f) y = 8

(g) No Solution. (h) x = 5

5


16. (a)

(b) d =1

2; M

✓�

1

2, 6

◆

(c) (x+ 2)2 + (y � 3)2 = 16; C(�2, 3); r = 4

17. (a) x2 +y

2

49= 1

(b)(x+ 4)2

4+

(y � 1)2

16= 1

6

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