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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