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

Accepted Answer

Even

Question 4

For the function $$y = 2\sin(x)$$, what is the amplitude and range?

Accepted Answer

Amplitude: $$2$$, Range: $$[-2, 2]$$

Question 5

What is the period of the function $$y = \sin(3x)$$?

Accepted Answer

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

Question 6

A sound wave is modeled by $$y = 4\cos(2x). $$What is the amplitude and period of this wave?

Accepted Answer

Amplitude: $$4$$, Period: $$\pi$$

Question 7

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

Accepted Answer

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

Question 8

If the midline of a sinusoidal function is $$y = -3$$, and the amplitude is $$5$$, what is the maximum value of the function?

Accepted Answer

$$2$$

Question 9

A Ferris wheel rotates such that the height $$h (in $$meters) of a seat above the ground at time $$t (in $$minutes) is modeled by $$h(t) = 10\sin(\pi t) + 15. $$What is the minimum height above the ground?

Accepted Answer

$$5$$ meters

Question 10

Given $$y = -2\sin(5x)$$, what is the amplitude and period?

Accepted Answer

Amplitude: $$2$$, Period: $$\dfrac{2\pi}{5}$$

Question 11

Which of the following best describes the effect of increasing the value of $$b in$$ $$y = a\sin(bx)$$?

Accepted Answer

The graph completes more cycles in the same interval, decreasing the period.

Question 12

A medical device uses a signal modeled by $$y = 3\cos(4x) - 2. $$What is the midline of this function?

Accepted Answer

$$y = -2$$

Question 13

If $$y = a\sin(bx + c) + d$$ has amplitude $$7$$, period $$\pi$$, and midline $$y = 2$$, what are the values of $$a$$, $$b$$, and $$d$$?

Accepted Answer

$$a = 7$$, $$b = 2$$, $$d = 2$$

Question 14

A city’s temperature over a day is modeled by $$T(t) = 8\cos\left(\dfrac{\pi}{12}t\right) + 65$$, where $$t is $$hours after midnight. What is the period of this function?

Accepted Answer

$$24$$ hours

Question 15

Which of the following is the correct formula for the period of $$y = a\sin(bx)$$?

Accepted Answer

$$\dfrac{2\pi}{b}$$

Question 16

If $$y = 5\sin(x) + 3$$, what is the range of the function?

Accepted Answer

$$[-2, 8]$$

Question 17

A light wave is modeled by $$y = 0.5\sin(6x - \pi). $$What is the phase shift of this function?

Accepted Answer

$$\dfrac{\pi}{6}$$ units to the right

Question 18

Which of the following statements about the amplitude of $$y = a\cos(bx) + d is $$true?

Accepted Answer

The amplitude is $$|a|$$, which is half the distance between the maximum and minimum values.

Question 19

If $$y = 3\sin(2x) - 4$$, what is the minimum value of the function?

Accepted Answer

$$-7$$

Precalculus Study Notes: Quadratic and Trigonometric Functions

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