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 $$y = 3\sin(2x)$$, what is the amplitude and period?

Accepted Answer

Amplitude: $$3$$, Period: $$\pi$$

Question 5

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

Accepted Answer

Frequency: $$4$$, Period: $$\dfrac{\pi}{2}$$

Question 6

What is the new range of $$y = 2\sin(x)$$ after the transformation compared to $$y = \sin(x)$$?

Accepted Answer

$$[-2, 2]$$

Question 7

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

Accepted Answer

Vertical shift (midline)

Question 8

A Ferris wheel rotates such that the height of a seat above the ground is modeled by $$h(t) = 10\cos\left(\dfrac{\pi}{15}t\right) + 12. $$What is the amplitude and what does it represent in this context?

Accepted Answer

Amplitude: $$10$$, representing the maximum deviation from the midline (12 feet) above or below.

Question 9

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

Accepted Answer

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

Question 10

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

Accepted Answer

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

Question 11

If $$y = \sin(\omega x)$$ and the period is $$\dfrac{2\pi}{\omega}$$, what is the period of $$y = \sin(7x)$$?

Accepted Answer

$$\dfrac{2\pi}{7}$$

Question 12

A city’s temperature over a year is modeled by $$T(t) = 15\sin\left(\dfrac{2\pi}{12}t - \dfrac{\pi}{3}\right) + 60. $$What is the midline and what does it represent?

Accepted Answer

Midline: $$y = 60$$, representing the average temperature.

Question 13

Which transformation will shift the graph of $$y = \sin(x) up by 3 $$units?

Accepted Answer

$$y = \sin(x) + 3$$

Question 14

If $$y = 2\cos(x)$$, what is the maximum and minimum value of the function?

Accepted Answer

Maximum: $$2$$, Minimum: $$-2$$

Question 15

A sinusoidal function has amplitude $$5$$ and midline $$y = -2. $$What is the range of the function?

Accepted Answer

$$[-7, 3]$$

Question 16

Which equation represents a cosine function with amplitude $$4$$, period $$\pi$$, and midline $$y = 1$$?

Accepted Answer

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

Question 17

A patient’s heart rate is modeled by $$H(t) = 20\sin(\pi t) + 80. $$What is the maximum heart rate predicted by this model?

Accepted Answer

$$100$$

Question 18

If $$y = \sin(x)$$ and $$y = \sin(3x)$$ are graphed on the same axes, how does the graph of $$y = \sin(3x)$$ compare to $$y = \sin(x)$$?

Accepted Answer

It completes three cycles in the interval $$[0, 2\pi].$$

Question 19

What is the effect of the negative sign in $$y = -2\sin(x)$$?

Accepted Answer

It reflects the graph over the x-axis.

Precalculus Study Notes: Quadratic and Trigonometric Function Attributes

Guida di studio - Domande di pratica

Study guide - Flashcard