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

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

Accepted Answer

Even

Question 4

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

Accepted Answer

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

Question 5

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

Accepted Answer

Vertical shift (midline)

Question 6

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

Accepted Answer

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

Question 7

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 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

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

Accepted Answer

Phase shift right by $$\frac{\pi}{2}$$

Question 10

A Ferris wheel rotates such that the height $$h (in $$meters) of a passenger 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 11

Given $$y = -3\cos(4x) + 2$$, what is the amplitude, period, and midline of the function?

Accepted Answer

Amplitude: $$3$$, Period: $$\dfrac{\pi}{2}$$, Midline: $$y=2$$

Question 12

If $$y = 5\sin(2x - \pi) - 4$$, what is the phase shift and vertical shift?

Accepted Answer

Phase shift: $$\dfrac{\pi}{2}$$ right, Vertical shift: $$-4$$

Question 13

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

Accepted Answer

The period decreases, so the graph repeats more frequently.

Question 14

A temperature sensor records data modeled by $$T(t) = 8\cos\left(\dfrac{\pi}{6}t\right) + 20. $$What is the period of the temperature cycle?

Accepted Answer

$$12$$

Question 15

Given $$y = 2\sin(5x)$$, what is the frequency and period of the function?

Accepted Answer

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

Question 16

If the maximum value of a sinusoidal function is $$7$$ and the minimum value is $$-1$$, what is the amplitude?

Accepted Answer

$$4$$

Question 17

Which equation represents a cosine function with amplitude $$3$$, period $$\pi$$, phase shift $$\dfrac{\pi}{4} to $$the right, and midline $$y = -2$$?

Accepted Answer

$$y = 3\cos\left(2(x - \dfrac{\pi}{4})\right) - 2$$

Precalculus Study Notes: Quadratic and Trigonometric Function Attributes

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