Question 1

Given the function $$y = 2\sin\left(\frac{x}{2} + \frac{\pi}{2}\right) + 1$$, what is the amplitude of the graph?

Accepted Answer

$$2$$

Question 2

What is the period of the function $$y = -\frac{1}{2}\cos\left(2x - \frac{\pi}{2}\right) - 3$$?

Accepted Answer

$$\pi$$

Question 3

A sinusoidal function $$h(	heta)$$ has a maximum at $$(\pi, 8)$$ and the first minimum after this maximum at $$(3\pi, -2). $$What is the midline of this function?

Accepted Answer

$$y = 3$$

Question 4

Given the function $$y = A\sin(Bx - C) + D$$, which transformation is applied first when graphing?

Accepted Answer

Vertical shift $$D$$

Question 5

A toy car travels around a circular track with a center 20 inches from a wall. The car starts at the wall and completes a lap every 8 seconds. What is the amplitude of the function modeling the distance from the wall?

Accepted Answer

$$20$$ inches

Question 6

For the function $$y = 3\sin(2x) + 3$$, what is the midline?

Accepted Answer

$$y = 3$$

Question 7

If the period of a cosine function is $$4\pi$$, what is the value of $$B in$$ $$y = A\cos(Bx)$$?

Accepted Answer

$$B = \frac{1}{2}$$

Question 8

A clock’s minute hand is 8 inches long and the center is 120 inches above the floor. If the hand moves twice as fast as normal, what is the period of the function modeling the height of the tip above the floor?

Accepted Answer

$$30$$ minutes

Question 9

Given $$y = -2\sin\left(x - \frac{\pi}{4}\right) + 1$$, what is the phase shift?

Accepted Answer

$$\frac{\pi}{4}$$ units to the right

Question 10

Which of the following best describes the behavior of $$g(	heta)$$ over the interval $$\frac{\pi}{2} \u003c 	heta \u003c \pi if$$ $$g(	heta) is a $$standard sine function?

Accepted Answer

Decreasing and concave down

Question 11

If $$y = 4\cos(2x) + 1$$, what is the frequency of the function?

Accepted Answer

$$2$$

Question 12

A sinusoidal function $$k(	heta)$$ has a minimum at $$\left(\frac{\pi}{2}, 0ight)$$ and a maximum at $$(\pi, 12). $$What is the amplitude?

Accepted Answer

$$6$$

Question 13

Which equation represents a cosine function with amplitude $$3$$, period $$\pi$$, and midline $$y = -2$$?

Accepted Answer

$$y = 3\cos(2x) - 2$$

Question 14

If $$y = -\sin(x)$$, which transformation has been applied to the parent sine function?

Accepted Answer

Reflection over the $$x-$$axis

Question 15

A sinusoidal function has a midline at $$y = 10$$, amplitude $$5$$, and period $$6. $$Which is a possible equation?

Accepted Answer

$$y = 5\sin\left(\frac{\pi}{3}x\right) + 10$$

Question 16

Which of the following intervals describes where the function $$h(t) ($$modeling the clock hand height) is both decreasing and concave up?

Accepted Answer

$$7.5 \u003c t \u003c 15$$

Question 17

If $$y = 2\sin(3x)$$, what is the period?

Accepted Answer

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

Question 18

Which of the following is the correct formula for the frequency of a sinusoidal function $$y = A\sin(Bx)$$?

Accepted Answer

$$\frac{B}{2\pi}$$

Question 19

A sinusoidal function $$h(t)$$ models the distance between a toy car and a wall, with period $$8$$ seconds and amplitude $$20$$ inches. What is the frequency?

Accepted Answer

$$\frac{1}{8}$$ 	ext{ Hz}$

Question 20

Given $$y = 2\cos\left(\frac{x}{3}\right) - 1$$, what is the period?

Accepted Answer

$$6\pi$$

Graphing Sine and Cosine Functions and Their Transformations

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