MAC 2311 Summer C 2016 Worksheet 2 (1.3, 1.4)

Group Names_____________________________________________________________________________

Determine an appropriate viewing window for the given function and use it to display its graph.

1) y = 4 16 + x2

161)

A) B)

C) D)

Graph the function.1

2) y = 5x + 15 2)

A) B)

C) D)

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3) y = (-5x)2/3 - 2 3)

A) B)

C) D)

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4) Graph the function f(x) = sin 4x + cos 2x. 4)

A) B)

C) D)

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5) y - 4 = x2/3 5)

A) B)

C) D)

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Using the graph below, find the domain and range of the given function, and sketch the graph.

6) y = f(-x - 2) + 1 6)

A) D: [-6, 3]; R: [-2, 4] B) D: [-7, 2]; R: [-2, 4]

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C) D: [-7, 2]; R: [-2, 4] D) D: [-3, 6]; R: [-2, 4]

7) y = -f(x) 7)

A) D: [-7, 2]; R: [-4, 2] B) D: [-5, 4]; R: [-3, 3]

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C) D: [-7.5, 1]; R: [-1, 5] D) D: [-4, 5]; R: [-3, 3]

The problem tells by what factor and direction the graph of the given function is to be stretched or compressed. Give anequation for the stretched or compressed graph.

8) y = x2 + 2 stretched horizontally by a factor of 4 8)

A) y = x2

16+ 2 B) y = 4x2 + 8 C) y = 16x2 + 2 D) y = x

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+ 2

9) y = x + 1 compressed vertically by a factor of 7 9)

A) y = x + 17

B) y = 7 x + 1 C) y = 7x + 7 D) y = 7x + 1

Graph the function in the ts-plane (t-axis horizontal, s-axis vertical). State the period and symmetry of the function.10) s = -tan 4t 10)

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A) Period 4

, symmetric about the origin B) Period 4

, symmetric about the origin

C) Period , symmetric about the origin D) Period 4

, symmetric about the s-axis

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Solve the problem.11) The accompanying figure shows the graph of y = x2 shifted to a new position. Write the equation

for the new graph.11)

A) y = x2 + 6 B) y = (x - 6)2 C) y = x2 - 6 D) y = (x + 6)2

12) If f(x) = x, g(x) = x5

, and h(x) = 5x+ 15, find h(g(f(x))). 12)

A) 5 x + 15 B) x + 3 C) x + 15 D) x + 3

13) Let g(x) = x + 5. Find a function y = f(x) so that (f g)(x) = 2x + 10 13)A) f(x) = 2x - 5 B) f(x) = 2x C) f(x) = 2(x + 1) D) f(x) = 2x + 5

Use a graphing calculator or computer to determine which of the given viewing windows displays the most appropriategraph of the specified function.

14) f(x) = |x2 - 4| 14)A) [-10, 10] by [-15, 15] B) [0, 5] by [-2, 10]C) [-5, 5] by [-15, 15] D) [-5, 5] by [-2, 10]

Express the given function as a composite of functions f and g such that y = f(g(x)).

15) y = 27x + 3

15)

A) f(x) = 2x

, g(x) = 7x + 3 B) f(x) = 2, g(x) = 7 + 3

C) f(x) = 2x

, g(x) = 7x + 3 D) f(x) = 7x + 3, g(x) = 2

State the period of the function and graph.

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16) cos x +3

16)

A) Period 2 B) Period 2

C) Period 2 D) Period 2

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17) sin 8x 17)

A) Period 4

B) Period 4

C) Period 4

D) Period 4

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18) cos x -4

+ 3 18)

A) Period 2 B) Period 2

C) Period 2 D) Period 2

The problem tells how many units and in what direction the graph of the given equation is to be shifted. Give anequation for the shifted graph. Then sketch the original graph with a dashed line and the shifted graph with a solid line.

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19) y = 1x

Down 5, right 4 19)

A) y + 5 = 1x - 4

B) y - 5 = 1x - 4

C) y - 5 = 1x + 4

D) y + 5 = 1x + 4

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20) x2 + y2 = 16 Up 1, right 4 20)

A) (x - 4)2 + (y - 1)2 = 16 B) (x + 4)2 + (y + 1)2 = 16

C) (x - 4)2 + (y + 1)2 = 16 D) (x + 4)2 + (y - 1)2 = 16

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