Question 1

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

Accepted Answer

It is odd, symmetric about the origin.

Question 2

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

Accepted Answer

$$2\pi$$

Question 3

Given the function $$f(x) = 3\sin(x - \frac{\pi}{2}) + 2$$, what is the amplitude?

Accepted Answer

$$3$$

Question 4

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

Accepted Answer

$$[-1, 1]$$

Question 5

A Ferris wheel rotates such that the height $$h (in $$meters) of a passenger above the ground at time $$t (in $$seconds) is modeled by $$h(t) = 10\sin(\frac{\pi}{15}t) + 12. $$What is the midline of this function?

Accepted Answer

$$y = 12$$

Question 6

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

Accepted Answer

A phase shift right by $$\frac{\pi}{3}$$ units.

Question 7

If $$f(x) = \cos x$$ and $$g(x) = 2\cos(x) - 1$$, what is the range of $$g(x)$$?

Accepted Answer

$$[-3, 1]$$

Question 8

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

Accepted Answer

Its x-intercepts occur at $$x = n\pi$$, where $$n is an $$integer.

Question 9

A sound wave can be modeled by $$y = 0.5\cos(4x). $$What is the period of this wave?

Accepted Answer

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

Question 10

Which of the following best describes the function $$f(x) = \cos(-x)$$?

Accepted Answer

It is an even function.

Question 11

Given $$f(x) = \sin x$$ and $$g(x) = \sin(x) + 2$$, how does the graph of $$g(x)$$ compare to $$f(x)$$?

Accepted Answer

It is shifted 2 units up.

Question 12

Which of the following is the equation of a cosine function with amplitude 4, period $$\pi$$, and midline $$y = -1$$?

Accepted Answer

$$y = 4\cos(2x) - 1$$

Question 13

A medical device uses a signal modeled by $$y = 2\sin(3x). $$What is the frequency of this signal?

Accepted Answer

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

Question 14

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

Accepted Answer

It passes through the origin.

Question 15

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

Accepted Answer

Reflection over the x-axis.

Question 16

A city’s daylight hours over a year can be modeled by $$D(t) = 3\sin(\frac{2\pi}{12}t - \frac{\pi}{3}) + 12$$, where $$t is $$the month. What is the phase shift of this function?

Accepted Answer

$$2$$ months to the right

Question 17

Which of the following is NOT a property of the parent sine function $$y = \sin x$$?

Accepted Answer

It is even.

Question 18

Given $$f(x) = \sin x$$ and $$g(x) = \sin(2x)$$, how does the graph of $$g(x)$$ compare to $$f(x)$$?

Accepted Answer

It has half the period of $$f(x).$$

Question 19

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

Accepted Answer

The height of a point on a rotating Ferris wheel over time.

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

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