Free Printable Transformations of Sine and Cosine Functions

1.

what is the amplitude of
y = 3sin (7x) -2

a)

7

b)

-2

c)

3

d)

6

2.

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

a)

a

b)

b

c)

c

d)

d

3.

What is the midline of this graph?

a)

y = 0

b)

y = -1

c)

y = -2

d)

y = -3

4.

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

5.

What is the period of the function $y=5\cos\left(\frac{1}{5}x\right)$

a)

10π

b)

$\frac{2\pi}{5}$

c)

$\frac{1}{5}$

d)

10

6.

Describe the shift: $y=\cos\left(x-\frac{\pi}{4}\right)$

a)

Up π

b)

Down $\frac{\pi}{4}$

c)

Left $\frac{\pi}{4}$

d)

Right $\frac{\pi}{4}$

7.

Which function represents the graph?

a)

f(x) = 3 sin x

b)

f(x) = 3 cos x

c)

f(x) = sin ( ⅓ x)

d)

f(x) = sin (3 x)

8.

a)

f(x) = 3 sin x

b)

f(x) = 3 cos x

c)

f(x) = sin (3 x)

d)

f(x) = cos (3 x)

9.

Where does the graph of y=sin(x) begin its first cycle?

a)

(0,0)

b)

(1,0)

c)

(0,Pi)

d)

(1, Pi)

10.

Where does the graph of cosine begin?

a)

(0,0)

b)

(0,1)

c)

(0, Pi)

d)

(1, Pi)

11.

What is the period of either graph?
y = sin(x) & y = cos (x)

a)

Pi

b)

2Pi

c)

Pi/2

d)

Pi/4

12.

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

a)

$\frac{2\pi}{5}$

b)

π

c)

5

d)

5π

13.

What is the period of
y= -3 sin(x)

a)

π

b)

2π

c)

3π

d)

4π

14.

What is the amplitude of
y = 3 cos 2x?

a)

3

b)

2

c)

90⁰

d)

350⁰

15.

What is the amplitude of the graph if each grid is scaled by 2?

a)

-2

b)

2

c)

4

d)

-4

16.

The __________ represents half the distance between the max and min of a sine or cosine graph.

a)

Period

b)

Frequency

c)

Extreme Values

d)

Amplitude

17.

What is the equation of the blue graph?

a)

y = 2sin x

b)

y = sin(2x)

c)

y = sin(x + 2)

d)

y = sin(x) - 2

18.

What is the range of y = sin x ?

a)

{-1 < y < 1}

b)

{-1 ≤ y ≤ 1}

c)

{-1 < x < 1}

d)

{-1 ≤ x ≤ 1}

19.

The function y = 2 sin θ transforms the parent function y = sin θ by _________________________

a)

stretching the graph vertically by a factor of 2

b)

translating the graph vertically up 2 units

20.

What is the amplitude and period of y = 2sin(3(x+4))

a)

Amplitude = 2

Period = 3

b)

Amplitude = 3

Period = 2

c)

Amplitude = 2

Period = 2π/3,

d)

Amplitude = 2π/3

Period = 2

21.

Describe the transformation:
$f\left(x\right)\ =\ \cos\left(x\ -\ \frac{\pi}{4}\right)$

a)

Up $\frac{\pi}{4}$

b)

Down $\frac{\pi}{4}$

c)

Left $\frac{\pi}{4}$

d)

Right $\frac{\pi}{4}$

22.

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

a)

It's always 2π

b)

$\frac{2\pi}{b}$

c)

$b\ \times\ 2\pi$

d)

$\frac{b}{2\pi}$

23.

What is the amplitude and period? $y\ =\ 2\sin\left[3\left(x+4\right)\right]$

a)

Amplitude = 2

Period = 3

b)

Amplitude = 3

Period = 2

c)

Amplitude = 2
Period = 2π/3

d)

Amplitude = 2π/3

Period = 2

24.

Write an equation for the cosine function with the following transformations:

amplitude = 3

period = $2\pi\$

phase shift: $\pi\ right$

vertical shift: up 5

a)

$y\ =\ 5\cos\left(x\ -\ \pi\right)\ +\ 3$

b)

$y\ =\ 3\cos\left(x-\pi\right)+5$

c)

$y\ =\ 5\cos\left(x\ +\ \pi\right)\ +\ 3$

d)

$y\ =\ 3\cos\left(x+\pi\right)+5$

25.

What is the equation of the blue graph?

a)

$y\ =\ \sin\left(3x\right)$

b)

$y\ =\ 3\sin x$

c)

$y\ =\ \sin x\ +\ 3$

d)

$y\ =\ -3\sin x$

26.

What is the phase shift?
$y\ =\ 4\cos\left(2x\ +\pi\right)-2$

a)

left $\frac{\pi}{2}$

b)

rightundefined

c)

right $\pi$

d)

left $\pi$

27.

Write the equation for a sine function with an amplitude of 6 and a period of $\frac{\pi}{4}$

a)

$y\ =\ 6\sin\left(8x\right)$

b)

$y\ =\ 6\sin\left(\frac{1}{8}x\right)$

c)

$y\ =\ 3\sin\left(8x\right)$

d)

$y\ =\ 3\sin\left(\frac{1}{8}x\right)$

28.

What is the period of the function $y=2\sin\ \frac{2}{3}x-1$ ?

a)

$\frac{2}{3}$

b)

2

c)

$\frac{2}{3}\pi$

d)

$3\pi$

29.

What is the maximum value of the function y = 10 sin [ 2 (x - 10) ] + 25 ?

a)

10

b)

20

c)

35

d)

30

30.

What is the phase shift for the function
f(x) = -2sin(4x + π) - 1

a)

π

b)

4π

c)

2π

d)

π⁄4

31.

What is the phase shift for y = 4cos(¹/₂x +π) - 2?

a)

left pi/2

b)

right pi/2

c)

right 2pi

d)

left 2pi

32.

In the equation $y\ =\ \frac{1}{3}\cos\left(\frac{1}{2}x+\frac{\pi}{3}\right)$ , what is the phase shift?

a)

$-\frac{2\pi}{3}$

b)

$\frac{2\pi}{3}$

c)

$\pi$

d)

$\pi$

33.

Examine the equation $y=-\cos\left(x-\frac{\pi}{4}\right)+2$ and the graph above. Does the graph represent the equation?

a)

Yes

b)

No

c)

Maybe

d)

What Graph?

34.

The period of a function is

a)

the length of one cycle

b)

how high and low the function goes from the center line

c)

the range of the function

35.

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

a)

A) y=6sin(8x)

b)

B) y=6sin8(x-1)

c)

C) y=6sin1/4x

d)

D) y=6sinx

36.

What is the shift for

y = 4 cos(x +π) - 2?

(Define your transformations first (a,b,c,d), and then determine which one of your answer choices matches the transformation for this function )

a)

A) up 2

b)

B) left 2

c)

C) right 2

d)

D) down 2

37.

a)

$period:\ 6\pi$

b)

$period:\ 3\pi$

c)

$period:\ 2\pi$

d)

$period:\ 8\pi$

38.

When a trig function is undefined there will be a ______________ that passes through that x-value.

a)

point

b)

vertical asymptote

c)

horizontal asymptote

d)

blank

39.

The phase shift is the same as ... ?

a)

vertical stretch/compression

b)

horizontal translation

c)

vertical translation

d)

reflection

40.

The period of the curve is:

a)

$2\pi$

b)

$3\pi$

c)

$4\pi$

d)

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

41.

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)

$y=3\cos x+2$

42.

What is the equation of the graph below:

a)

$y=4\sin\left(\theta-\frac{\pi}{2}\right)+1$

b)

$y=-4\cos\left(2\theta+\frac{\pi}{4}\right)+1$

c)

$y=4\cos\left(2\theta-\frac{\pi}{2}\right)+1$

d)

$y=-4\sin\left(2\theta\right)+1$

43.

Which graph shows $y=4\sin\left(\frac{x}{4}+\frac{3\pi}{4}\right)-1$

a)

b)

c)

d)

44.

Which graph shows $y=3\sin\left(2x-\frac{\pi}{4}\right)-1$

a)

b)

c)

d)

45.

What is the minimum value of the follow equation:

$y=-7\cos\left(2x-\frac{\pi}{2}\right)-4$

a)

y = -4

b)

y = -11

c)

y = 3

d)

y = -3

46.

What is the minimum value of the follow equation:

$y=-5\sin\left(\frac{1}{2}x+\pi\right)+8$

a)

y = 8

b)

y = -13

c)

y = 3

d)

y = 13

47.

True or False: The domain for any sine and cosine graph will always be All Real Numbers $\left(-\infty,\ \infty\right)$

a)

True

b)

False

48.

Select which trig. functions have asymptotes on their graphs

a)

cosine

b)

sine

c)

tangent

d)

cosecant

e)

secant

49.

True or False: Sine and cosine graphs are identical except for different phase shifts

a)

True

b)

False

50.

Which equation below is NOT possible for the graph?

a)

$y=\cos\left(x\right)-2$

b)

$y=-\cos\left(x+180\degree\right)-2$

c)

$y=\sin\left(x+270\degree\right)-2$

d)

$y=-\sin\left(x-90\degree\right)-2$

51.

Which equation is NOT possible for the graph?

a)

$y=-2+3\cos\left(\frac{1}{2}x+\frac{\pi}{4}\right)$

b)

$y=-2-3\cos\left(\frac{1}{2}x-\frac{3\pi}{2}\right)$

c)

$y=3\sin\left(\frac{1}{2}x+\frac{3\pi}{4}\right)-2$

d)

$y=-3\sin\left(\frac{1}{2}x-\frac{\pi}{4}\right)-2$

52.

What is a correct interval of decrease?

a)

$\left(-\frac{3\pi}{4},\ -\frac{\pi}{4}\right)$

b)

$\left(-\frac{3\pi}{2},\ \frac{\pi}{2}\right)$

c)

$\left(-\frac{3\pi}{2},\ \frac{-\pi}{2}\right)$

d)

$\left(-\frac{\pi}{4},\ \frac{\pi}{4}\right)$

53.

What is a correct interval of deccrease?

a)

$\left(-\frac{3\pi}{4},\ -\frac{\pi}{4}\right)$

b)

$\left(-\frac{3\pi}{2},\ \frac{\pi}{2}\right)$

c)

$\left(-\frac{3\pi}{2},\ -\frac{\pi}{2}\right)$

d)

$\left(-\frac{\pi}{4},\ \frac{\pi}{4}\right)$

54.

What are two valid interval of decrease?

a)

$\left(0\degree,\ 180\degree\right)$

b)

$\left(180\degree,\ 360\degree\right)$

c)

$\left(360\degree,\ 540\degree\right)$

d)

$\left(540\degree,\ 720\degree\right)$

55.

What are two valid interval of increase?

a)

$\left(0\degree,\ 180\degree\right)$

b)

$\left(180\degree,\ 360\degree\right)$

c)

$\left(360\degree,\ 540\degree\right)$

d)

$\left(-180\degree,\ 0\degree\right)$

Transformations of Sine and Cosine Functions

Total questions: 55

Worksheet time: 3585secs

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