Question 1

Which of the following best describes the symmetry of the function $$f(x) = \sin x$$?

Accepted Answer

It is symmetrical about the origin (odd function).

Question 2

What is the amplitude of the function $$f(x) = 3 \cos x$$?

Accepted Answer

$$3$$

Question 3

Given the function $$f(x) = \sin(x - \frac{\pi}{2})$$, what transformation has occurred compared to $$f(x) = \sin x$$?

Accepted Answer

A horizontal shift right by $$\frac{\pi}{2}$$ units.

Question 4

What is the period of the function $$f(x) = \cos(2x)$$?

Accepted Answer

$$\pi$$

Question 5

Which of the following is the correct range for $$f(x) = \sin x$$?

Accepted Answer

$$[-1, 1]$$

Question 6

A sound wave can be modeled by $$y = 2 \sin(3x). $$What is the amplitude and period of this wave?

Accepted Answer

Amplitude: $$2$$, Period: $$\frac{2\pi}{3}$$

Question 7

Which equation represents a cosine function that has been reflected over the x-axis and shifted up by 4 units?

Accepted Answer

$$y = -\cos x + 4$$

Question 8

If $$f(x) = \sin x$$ and $$g(x) = \cos x$$, which statement is true about their graphs?

Accepted Answer

The graph of $$g(x) is a $$horizontal shift of $$f(x) to $$the left by $$\frac{\pi}{2}.$$

Question 9

Which of the following functions is even?

Accepted Answer

$$f(x) = \cos x$$

Question 10

A Ferris wheel rotates such that the height of a passenger above the ground can be modeled by $$h(t) = 10 + 5 \sin(\frac{\pi}{6} t)$$, where $$t is $$time in seconds. What is the maximum height reached?

Accepted Answer

$$15$$ meters

Question 11

Which transformation is applied to $$y = \sin x to $$obtain $$y = \sin(x) + 2$$?

Accepted Answer

Vertical shift up by 2 units.

Question 12

What is the x-intercept of the function $$f(x) = \cos x in $$the interval $$[0, 2\pi]$$?

Accepted Answer

$$x = \frac{\pi}{2}$$ and $$x = \frac{3\pi}{2}$$

Question 13

Which of the following best describes the domain of $$f(x) = \sin x$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 14

If $$y = 2 \sin(x - \pi)$$, what is the phase shift and amplitude?

Accepted Answer

Phase shift: $$\pi$$ left, Amplitude: $$2$$

Question 15

Which function has a period of $$4\pi$$?

Accepted Answer

$$f(x) = \sin(\frac{x}{2})$$

Question 16

A medical device uses a signal modeled by $$y = 0.5 \cos(\pi t). $$What is the period of the signal?

Accepted Answer

$$1$$

Question 17

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

Accepted Answer

It passes through the origin and has a maximum at $$x = \frac{\pi}{2}.$$

Question 18

Which equation represents a sine function with amplitude $$4$$, period $$\pi$$, and phase shift $$\frac{\pi}{4} to $$the right?

Accepted Answer

$$y = 4 \sin(2x - \frac{\pi}{4})$$

Question 19

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

Accepted Answer

It is an even function.

Graphing Sine and Cosine Functions: Attributes, Symmetry, and Transformations

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