Question 1

Which of the following best describes the amplitude of the function $$y = 5 \sin(x)$$?

Accepted Answer

$$5$$

Question 2

What is the period of the function $$y = \sin(4x)$$?

Accepted Answer

$$\frac{2\pi}{4} = \frac{\pi}{2}$$

Question 3

Given the function $$y = -3 \sin(x)$$, which transformation(s) are applied to the basic sine function?

Accepted Answer

Vertical stretch by 3 and vertical reflection

Question 4

For the function $$y = \sin(x) + 7$$, what is the effect on the graph compared to $$y = \sin(x)$$?

Accepted Answer

Shifted up by 7 units

Question 5

What is the range of the function $$y = -2 \sin(x) + 3$$?

Accepted Answer

$$[1, 5]$$

Question 6

Which of the following is the correct formula for the period of $$y = a \sin(bx + c) + d$$?

Accepted Answer

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

Question 7

If $$y = \sin(x - \frac{\pi}{2})$$, what is the phase shift of the function?

Accepted Answer

Shifted right by $$\frac{\pi}{2}$$

Question 8

Which of the following statements is true about the graph of $$y = \sin(x)$$?

Accepted Answer

It is symmetric about the origin

Question 9

A sound wave is modeled by $$y = 2 \sin(3x) + 4. $$What is the maximum value of the wave?

Accepted Answer

$$6$$

Question 10

For the function $$y = \sin(2x) - 5$$, what is the minimum value?

Accepted Answer

$$-6$$

Question 11

Which of the following describes the transformation for $$y = \sin(x + \pi)$$?

Accepted Answer

Shifted left by $$\pi$$

Question 12

What is the amplitude and period of $$y = 4 \sin(\frac{x}{2})$$?

Accepted Answer

Amplitude: $$4$$, Period: $$4\pi$$

Question 13

Which function has a vertical reflection and a vertical shift down by 4 units?

Accepted Answer

$$y = -\sin(x) - 4$$

Question 14

A medical device uses the function $$y = 3 \sin(2x - \pi) + 1 to $$model a periodic signal. What is the phase shift?

Accepted Answer

Right by $$\frac{\pi}{2}$$

Question 15

Which of the following is the correct general form for a sine function with amplitude $$a$$, period $$\frac{2\pi}{b}$$, phase shift $$c$$, and vertical shift $$d$$?

Accepted Answer

$$y = a \sin(bx + c) + d$$

Question 16

For the function $$y = \cos(x)$$, what is the value of $$y$$ when $$x = 0$$?

Accepted Answer

$$1$$

Question 17

Which of the following is true about the graph of $$y = \cos(x)$$ compared to $$y = \sin(x)$$?

Accepted Answer

It is a horizontal shift of $$\frac{\pi}{2} to $$the left

Question 18

A chemical reaction oscillates according to $$y = 2 \cos(3x) - 1. $$What is the minimum value of the function?

Accepted Answer

$$-3$$

Question 19

What is the period of $$y = \cos(\frac{x}{3})$$?

Accepted Answer

$$6\pi$$

Graphing Sine and Cosine Functions: Amplitude, Period, Phase Shift, and Vertical Shift

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