Graphing

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Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Match the function with its graph. 1) 1) y = sin x 2) y = cos x 3) y = -sin x 4) y = -cos x

1)

A)

B) 3

-2∏

y

3

2

2

1

1

-∏



2∏

x

-2∏

-∏



-1

-1

-2

-2

-3

-3

C)

y

2∏

x

D) 3

-2∏

y

3

2

2

1

1

-∏



2∏

x

-2∏

-∏



-1

-1

-2

-2

-3

-3

A) 1B, 2D, 3C, 4A

y

B) 1A, 2B, 3C, 4D

2∏

C) 1C, 2A, 3B, 4D

1

x

D) 1A, 2D, 3C, 4B

2) 1) y = sin 3x 2) y = 3 cos x 3) y = 3 sin x 4) y = cos 3x

2)

A)

B) 3

-2∏

-∏

y

3

2

2

1

1



-1

2∏

x

-2∏

-∏

-1

-2

-2

-3

-3

C)



2∏



2∏

x

D) y

-2∏

y

-∏

y

3

3

2

2

1

1

-1



2∏

x

-2∏

-∏

-1

-2

-2

-3

-3

A) 1A, 2C, 3D, 4B

B) 1B, 2D, 3C, 4A

C) 1A, 2B, 3C, 4D

2

x

D) 1A, 2D, 3C, 4B

3) 1) y = sin 3) y =

1 x 2

2) y =

1 sin x 2

1 cos x 2

4) y = cos

1 x 2

A)

B) 3

-2∏

3)

-∏

y

3

2

2

1

1



-1

2∏

x

-2∏

-∏

-2

-1



2∏



2∏

x

-2

-3

-3

C)

D) 3

-2∏

y

y

3

2

2

1

1

-∏



2∏

x

-2∏

-∏

-1

-1

-2

-2

-3

-3

A) 1A, 2D, 3C, 4B

B) 1A, 2C, 3D, 4B

y

x

C) 1B, 2D, 3C, 4A

3

D) 1A, 2B, 3C, 4D

4) 1) y = 1 + sin x 3) y = -1 + sin x

2) y = 1 + cos x 4) y = -1 + cos x

A)

B) 3

-2∏

-∏

y

3

2

2

1

1



-1

2∏

x

-2∏

-∏

y

-1

-2

-2

-3

-3

C)



2∏



2∏

x

D) 3

-2∏

4)

y

3

2

2

1

1

-∏



2∏

x

-2∏

-∏

-1

-1

-2

-2

-3

-3

A) 1A, 2C, 3D, 4B

B) 1A, 2D, 3C, 4B

y

x

C) 1B, 2D, 3C, 4A

4

D) 1A, 2B, 3C, 4D

5) 1) y = sin x -

p 2

2) y = cos x +

p 2

3) y = sin x +

p 2

4) y = cos x -

p 2

A)

5)

B) 3

-2∏

y

3

2

2

1

1

-∏



2∏

x

-2∏

-∏

-1

-1

-2

-2

-3

-3

C)

y



2∏



2∏

x

D) 3

-2∏

y

3

2

2

1

1

-∏



2∏

x

-2∏

-∏

-1

-1

-2

-2

-3

-3

A) 1A, 2D, 3C, 4B

y

B) 1A, 2B, 3C, 4D

x

C) 1C, 2A, 3B, 4D

D) 1B, 2D, 3C, 4A

Find the amplitude or period as requested. 6) Find the amplitude of y = -2 cos 4x + A) 2

B)

p . 2

6)

p 2

C) 4

D) -8

7) Find the amplitude of y = 5 cos (4x - p). A) 5

B) 4

8) Find the period of y = -2 sin 6x + A)

p 3

7) C) 20

D) p

p . 3

8)

B) p

C) 6

5

D) 2

9) Find the period of y = -5 sin A) 5p

1

3

x-

p . 2

9)

B) 6p

C)

p 2

D) 3p

Find the phase shift of the function. p 10) y = sin x + 2

10)

A)

p units to the right 2

B)

p units to the left 2

C)

p units up 2

D)

p units down 2

11) y = 5 sin 4x -

p 2

11)

A)

p units to the right 8

B) 5p units up

C)

p units to the left 2

D) 4p units down

12) y = 3 cos (8x + p)

12)

A) 8p units to the right C)

B)

p units to the left 3

p units to the left 8

D) 3p units to the right

Find the specified quantity. 13) Find the amplitude of y = -5 cos 3x + A) 3

B)

p 2

C) -15 p 2

14)

B) p

B)

D) 5

.

15) Find the vertical translation of y = -2 - 2 sin 6x + A) -2

13)

p 2

14) Find the period of y = 3 sin 4x + A)

p . 2

C) 3

D) 4

p . 2

p 2

15) C)

6

1 2

D) 2

Graph the function over a one-period interval. p 16) y = -2cos x + 2 3

16)

y

2 1

∏ 2

-1

3∏ 2



2∏

x

-2 -3

A)

B) 3

y

3

2

2

1

1

∏ 2

-1



3∏ 2

2∏

y

x -1

-2

-2

-3

-3

C)

∏ 2



3∏ 2

2∏

∏ 2



3∏ 2

2∏

x

D) 3

y

3

2

2

1

1

-1

∏ 2



3∏ 2

2∏

x -1

-2

-2

-3

-3

y

x

Solve the problem. 17) The voltage E in an electrical circuit is given by E = 3.4 cos 100pt, where t is time measured in seconds. Find the period. 1 p A) 50 B) 50p C) D) 50 50

17)

18) The voltage E in an electrical circuit is given by E = 5.7 cos 30pt, where t is time measured in seconds. Find the amplitude.

18)

A) 11.4

B) 5.7

C) 30 7

D) 30p

19) Suppose that the average monthly low temperatures for a small town are shown in the table. Month 1 2 3 4 5 6 7 8 9 10 11 12 Temperature (e F) 22 32 40 52 60 64 61 55 44 31 24 18

19)

Model this data using f(x) = a sin(b(x - c)) + d. A) f(x) = 23 sin

p x - 5 + 41

B) f(x) = 25 sin

p x - 4 + 44

C) f(x) = 23 sin

p (x-3) + 41

D) f(x) = 23 sin

p x - 4 + 41

6 6

6 6

20) Use regression to find constants a, b, c, and d so that f(x) = a sin (bx + c) + d models the data given below. Month 1 2 3 4 5 6 7 8 9 10 11 12 Precipitation (inches) 1 3 6 9 11 12 11 9 7 5 3 2 A) 4.708150061; 1.025102863; -2.474285177; 7.076487153 B) 5.099259265; 0.5315780435; -1.738394218; 8.659926499 C) 5.277184939; 0.06297637; -2.04256248; 6.904195597 D) 5.099259265; 0.5315780435; -1.738394218; 6.659926499

8

20)

Answer Key Testname: CHAPTER 8 GRAPHING

1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20)

C B C C C A A A B B A B D A A A C B C D

9

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