Question 1

Which of the following best describes the period of the function $$y = rac{1}{2} 	ext{sin}(4x)$$?

Accepted Answer

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

Question 2

Given the function $$y = 3 - 2\cos(3x)$$, what is the amplitude of the graph?

Accepted Answer

$$2$$

Question 3

A temperature in a city varies between $$60^\circF $$and $$80^\circF $$throughout the year and can be modeled by a sine function. What is the vertical shift $$c in $$the model $$f(x) = a\sin(b(x-d)) + c$$?

Accepted Answer

$$70$$

Question 4

What is the effect on the graph of $$y = \sin(x) if it is $$transformed to $$y = \sin(x - \frac{\pi}{4})$$?

Accepted Answer

It is shifted $$\frac{\pi}{4}$$ units to the right.

Question 5

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

Accepted Answer

It is an even function.

Question 6

If $$y = -2\sin(3x)$$, which statement is correct?

Accepted Answer

The period is $$\frac{2\pi}{3}.$$

Question 7

A sinusoidal function has a maximum value of $$10$$ and a minimum value of $$2. $$What is its amplitude?

Accepted Answer

$$4$$

Question 8

Which equation represents a sine function with amplitude $$5$$, period $$\pi$$, and shifted $$2$$ units up?

Accepted Answer

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

Question 9

The function $$y = 1 + 3\cos(2(x - \frac{\pi}{3})) is $$best described as:

Accepted Answer

A cosine function with amplitude $$3$$, period $$\pi$$, shifted right $$\frac{\pi}{3}$$ and up $$1$$ unit.

Question 10

Which of the following real-world phenomena can best be modeled by a cosine function?

Accepted Answer

The height of a Ferris wheel seat as it rotates.

Question 11

Given $$y = 2\sin(\frac{1}{2}x)$$, what is the period of the function?

Accepted Answer

$$4\pi$$

Question 12

Which transformation will change $$y = \sin(x) to$$ $$y = -\sin(x)$$?

Accepted Answer

Reflection across the x-axis.

Question 13

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

Accepted Answer

$$[2, 6]$$

Question 14

A sine function models daylight hours in a city, with a maximum of $$16$$ hours and a minimum of $$8$$ hours. What is the midline of the function?

Accepted Answer

$$y = 12$$

Question 15

Which of the following is the general form for a sinusoidal function?

Accepted Answer

$$y = c + a\sin[b(x - d)]$$

Question 16

If $$y = \sin(2x)$$, how many complete cycles does the graph make from $$x = 0 to$$ $$x = 2\pi$$?

Accepted Answer

2

Question 17

Which of the following describes the symmetry of the sine function?

Accepted Answer

Odd function, symmetric with respect to the origin.

Question 18

A sinusoidal function $$y = a\sin(bx) + c$$ has amplitude $$7$$, period $$6$$, and midline $$y = -2. $$What is the value of $$b$$?

Accepted Answer

$$\frac{2\pi}{6}$$

Question 19

Which of the following best describes the transformation from $$y = \cos(x) to$$ $$y = \cos(x) + 4$$?

Accepted Answer

Vertical shift upward by 4 units.

9.3 Graphs of Sine and Cosine Functions: Periodic Behavior, Transformations, and Applications

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