Question 1

What is the vertex of the function $$f(x) = -(x-4)^2$ - 1$$?

Accepted Answer

$$(4, -1)$$

Question 2

What is the range of the function $$f(x) = -(x-4)^2$ - 1$$?

Accepted Answer

$$(-\infty, -1]$$

Question 3

Given $$f(x) = 2x^4$ - x^2$ + 5$$, determine whether the function is even, odd, or neither.

Accepted Answer

Even

Question 4

For the function $$y = a\sin(b(x-c)) + d$$, what does the parameter $$a$$ represent?

Accepted Answer

Amplitude

Question 5

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

Accepted Answer

$$3$$

Question 6

What is the period of the function $$y = \sin(5x)$$?

Accepted Answer

$$\dfrac{2\pi}{5}$$

Question 7

A sound wave can be modeled by $$y = 4\sin(2x). $$What is the maximum value of the wave?

Accepted Answer

$$4$$

Question 8

If the midline of a sinusoidal function is $$y = -2$$, and the amplitude is $$5$$, what is the range of the function?

Accepted Answer

$$[-7, 3]$$

Question 9

For the function $$y = 2\sin(x) + 1$$, what is the new range after the transformation?

Accepted Answer

$$[-1, 3]$$

Question 10

A Ferris wheel rotates such that the height $$h (in $$meters) of a seat above the ground at time $$t (in $$seconds) is modeled by $$h(t) = 10\cos\left(\dfrac{\pi}{15}t\right) + 12. $$What is the period of the motion?

Accepted Answer

$$30$$

Question 11

Given $$y = 2\sin(x)$$, what is the frequency of the function?

Accepted Answer

$$1$$

Question 12

Which transformation occurs when the equation $$y = \sin(x) is $$changed to $$y = \sin(x - \frac{\pi}{2})$$?

Accepted Answer

A phase shift to the right by $$\frac{\pi}{2}$$ units

Question 13

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

Accepted Answer

$$\dfrac{2\pi}{3}$$

Question 14

A medical device uses a signal modeled by $$y = 0.5\sin(4x). $$What is the amplitude and period of the signal?

Accepted Answer

Amplitude: $$0.5$$, Period: $$\dfrac{2\pi}{4}$$

Question 15

Which of the following best describes the midline of the function $$y = -3\sin(x) + 2$$?

Accepted Answer

$$y = 2$$

Question 16

A sinusoidal function has amplitude $$A = 7$$ and midline $$y = -4. $$What is the minimum value of the function?

Accepted Answer

$$-11$$

Question 17

If $$y = \sin(2x)$$ and $$y = \sin(5x)$$ are graphed on the same axes, which statement is true about their periods?

Accepted Answer

$$y = \sin(5x)$$ has a shorter period than $$y = \sin(2x)$

Question 18

A city’s temperature over a year can be modeled by $$T(t) = 15\cos\left(\dfrac{2\pi}{12}t\right) + 60$$, where $$t is in $$months. What is the amplitude of the temperature variation?

Accepted Answer

$$15$$

Question 19

What is the effect of the transformation $$y = \sin(x) 	o y = 2\sin(x) - 3 on $$the graph?

Accepted Answer

Vertical stretch by 2 and shift down by 3

Question 20

Given $$y = \cos(x)$$, what is the frequency of the function?

Accepted Answer

$$1$$

Precalculus Study Notes: Quadratic and Trigonometric Function Attributes

Study Guide - Practice Questions

Study Guide - Flashcards