Question 1

What is the amplitude of the function $$y = -4 \sin(2x) + 3$$?

Accepted Answer

$$4$$

Question 2

Given $$y = 2 \cos\left(\frac{\pi}{3}x - \frac{\pi}{6}\right)$$, what is the period of the function?

Accepted Answer

$$6$$

Question 3

Which of the following equations represents a sine function with amplitude $$5$$, period $$\pi$$, and midline $$y = -2$$?

Accepted Answer

$$y = 5 \sin(2x) - 2$$

Question 4

What is the phase shift of $$y = 3 \cos\left(4x + \frac{\pi}{2}\right)$$?

Accepted Answer

$$\frac{\pi}{8}$$ units to the left

Question 5

If $$y = -2 \sin(x)$$, which transformation has occurred compared to $$y = \sin(x)$$?

Accepted Answer

Vertical stretch by $$2$$ and reflection across the x-axis

Question 6

A sound wave can be modeled by $$y = 0.5 \cos(6\pi t). $$What is the frequency of the wave?

Accepted Answer

$$3$$

Question 7

Which of the following best describes the midline of $$y = 7 \sin(2x) - 4$$?

Accepted Answer

$$y = -4$$

Question 8

Given the function $$y = 3 \cos(2x - \pi) + 1$$, what is the maximum value of the function?

Accepted Answer

$$4$$

Question 9

A Ferris wheel is modeled by $$y = 10 \sin\left(\frac{\pi}{15} t\right) + 12. $$What is the period of the wheel's rotation?

Accepted Answer

$$30$$

Question 10

Which transformation occurs when the equation $$y = \sin(x) is $$changed to $$y = \sin(x - \frac{\pi}{3})$$?

Accepted Answer

Phase shift right by $$\frac{\pi}{3}$$

Question 11

What is the range of $$y = -2 \cos(x) + 1$$?

Accepted Answer

$$[-1, 3]$$

Question 12

Given the parameters amplitude $$= \frac{\pi}{7}$$, period $$= \frac{3}{7}$$, and phase shift $$= -\frac{1}{4}$$, which equation matches these values in the form $$y = a \cos[b(x - c)]$$?

Accepted Answer

$$y = \frac{\pi}{7} \cos\left(\frac{14\pi}{3}\left(x + \frac{1}{4}\right)\right)$$

Question 13

If $$y = 2 \sin(3x) + 4$$, what is the minimum value of the function?

Accepted Answer

Question 14

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

Accepted Answer

It is an even function symmetric about the y-axis.

Question 15

A temperature sensor records data modeled by $$y = 8 \sin\left(\frac{\pi}{12} t - \frac{\pi}{3}\right) + 20. $$What is the midline of this function?

Accepted Answer

$$y = 20$$

Question 16

Which of the following describes the effect of $$B \u003c 0 in$$ $$y = A \sin(Bx)$$?

Accepted Answer

The graph is reflected horizontally.

Question 17

If $$y = 4 \cos(2x) - 5$$, what is the range of the function?

Accepted Answer

$$[-9, -1]$$

Question 18

Which of the following is the correct formula for the period of $$y = A \sin(Bx - C) + D$$?

Accepted Answer

$$P = \frac{2\pi}{|B|}$$

Question 19

A daylight model is $$y = 3 \sin\left(\frac{\pi}{6} t\right) + 10. $$How many hours does it take to complete one cycle?

Accepted Answer

$$12$$

Graphs and Transformations of Sine and Cosine Functions

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