Free Printable Transformations of Trig Functions

1.

The __________ represents the distance above or below the midline of a sine or cosine graph; we always take the absolute value of this height.

a)

Period

b)

Vertical Shift

c)

Phase Shift

d)

Amplitude

2.

The period of a sine or cosine graph can be found by ....

a)

It's always 2π

b)

2π/B

c)

B(2π)

d)

2π+B

3.

Which value represents a vertical shift in the following function y=a*sin(bx - c)+d?

a)

a

b)

b

c)

c

d)

d

4.

Which value helps identify the period in the following function y=a*sin(bx-c)+d?

a)

a

b)

b

c)

c

d)

d

5.

What is the period of
y=cos(3x - π) - 5?

a)

π/3

b)

π/6

c)

2π/3

d)

2π/6

6.

Where is the midline for

y=2cos(1/3x +π/6) +2

a)

y = 1/3

b)

y = -2

c)

y = 2

d)

y = 4

7.

What is the period of y=4cos(5x)

a)

2π/5

b)

π

c)

5π/2

d)

5π

8.

What does a negative A value cause?

a)

A negative amplitude

b)

A reflection across the Y axis

c)

No effect

d)

A reflection across X axis

9.

What is the amplitude of the function
f(x) = -3cos x ?

a)

-3

b)

3

c)

6

d)

-6

10.

Choose the correct equation for the graph.

a)

$y=\sin\left(x\right)$

b)

$y=\sec\left(x\right)$

c)

$y=\csc\left(x\right)$

d)

$y=\tan\left(x\right)$

e)

$y=\cot\left(x\right)$

11.

Choose the correct equation for the graph.

a)

$y=\sin\left(x\right)$

b)

$y=\sec\left(x\right)$

c)

$y=\csc\left(x\right)$

d)

$y=\tan\left(x\right)$

e)

$y=\cos\left(x\right)$

12.

Choose the correct equation for the graph.

a)

$y=\cot\left(x\right)$

b)

$y=\sec\left(x\right)$

c)

$y=\csc\left(x\right)$

d)

$y=\tan\left(x\right)$

e)

$y=\cos\left(x\right)$

13.

$Which\ of\ the\ functions\ does\ NOT\ have\ a\ period\ of\ 2\pi$

a)

y = sin x

b)

y = tan x

c)

y = csc x

14.

What is the phase shift?
y=-2sin(x-π)

a)

π left

b)

π right

c)

none

d)

2π right

15.

What is the amplitude of the graph?

a)

-3

b)

2

c)

-2

d)

3

16.

What is the equation of the midline of the graph?

a)

y = -1

b)

y = 0

c)

y = 3

d)

y = -3

17.

Let f(t) = sin(t) and g(t) = sin(4t). What transformation of f(t) results in g(t)?

a)

Vertical Stretch

b)

Horizontal Stretch

c)

Vertical Compression

d)

Horizontal Compression

18.

Let f(t) = sin(t) and g(t) = sin(t - 4). What transformation of f(t) results in g(t)?

a)

Vertical shift down 4

b)

Horizontal shift right 4

c)

Vertical shift up 4

d)

Horizontal shift left 4

19.

The period of the curve is:

a)

$2\pi$

b)

$3\pi$

c)

$4\pi$

d)

$\frac{1}{2}\pi$

20.

What is the period of the equation shown?

a)

3π

b)

2π

c)

3π / 2

d)

2π / 3

21.

Describe the horizontal and vertical shifts.

a)

right 3π/2 , down 5

b)

left 2π/3 , up 5

c)

right 2π/3 , up 5

d)

left 2π , down 5

22.

Write the equation for a sine function with an amplitude of 6 and a period of π/4.

a)

y=6sin(8x)

b)

y=6sin8(x-1)

c)

y=6sin1/4x

d)

y=6sinx

23.

What is the vertical shift for $y=4\cos\frac{1}{2}\left(x+\pi\right)-2$ ?

a)

up 2

b)

left 2

c)

right 2

d)

down 2

24.

Write the equation of a cosine graph given the following:
Midline: y = 0
Amplitude = 3
Reflection over the x-axis
No Phase Shift
Period = $\pi$

a)

$y=-3\cos2x$

b)

$y=-3\cos\pi x$

c)

$y=-3\cos x$

d)

$y=3\cos x+2$

25.

What are the amplitude and the period of the graph represented by the equation $y=-3\cos\ \frac{\theta}{3}$ ?

a)

amplitude: -3 ; period: $\frac{\pi}{3}$

b)

amplitude: -3; period: $6\pi$

c)

amplitude: 3; period: $\frac{\pi}{3}$

d)

amplitude: 3; period: $6\pi$

Transformations of Trig Functions

Total questions: 25

Worksheet time: 18mins

Similar Resources on Wayground