Question 1

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

Accepted Answer

$$3$$

Question 2

Given the function $$y = 2 \sin\left(\frac{1}{2}x - \pi\right) + 1$$, what is the period?

Accepted Answer

$$4\pi$$

Question 3

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

Accepted Answer

Amplitude: $$0.5$$, Period: $$\frac{\pi}{2}$$

Question 4

Which transformation shifts the graph of $$y = \sin(x) up by$$ $$3$$ units and to the right by $$\frac{\pi}{2}$$ units?

Accepted Answer

$$y = \sin(x - \frac{\pi}{2}) + 3$$

Question 5

If $$y = a \sin(b(x - c)) + d$$, which parameter controls the vertical shift of the graph?

Accepted Answer

$$d$$

Question 6

A Ferris wheel rotates such that the height of a passenger above the ground is modeled by $$h(t) = 10 \sin\left(\frac{\pi}{5}t\right) + 12. $$What is the maximum height reached?

Accepted Answer

$$22$$ units

Question 7

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

Accepted Answer

$$\frac{2\pi}{|b|}$$

Question 8

The function $$y = -2 \cos(3x) + 1$$ models the temperature variation in a chemical reaction over time. What is the midline of this function?

Accepted Answer

$$y = 1$$

Question 9

Which of the following graphs represents a sine function with amplitude $$2$$, period $$\pi$$, and midline $$y = -1$$?

Accepted Answer

$$y = 2 \sin(2x) - 1$$

Question 10

A patient’s heart rate is modeled by $$H(t) = 5 \cos\left(\frac{\pi}{6}t - \frac{\pi}{2}\right) + 70. $$What is the amplitude and the vertical shift?

Accepted Answer

Amplitude: $$5$$, Vertical shift: $$70$$

Question 11

Which transformation will reflect the graph of $$y = \sin(x)$$ over the $$x-$$axis?

Accepted Answer

$$y = -\sin(x)$$

Question 12

If $$y = 3 \sin(2(x - \frac{\pi}{4}))$$, what is the phase (horizontal) shift?

Accepted Answer

$$\frac{\pi}{4}$$ units to the right

Question 13

A city’s daylight hours over a year can be modeled by $$D(t) = 2 \cos\left(\frac{2\pi}{365}t\right) + 12. $$What is the period in days?

Accepted Answer

$$365$$ days

Question 14

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

Accepted Answer

It starts at the midline and increases

Question 15

Given $$y = 4 \cos(\frac{1}{3}x) - 2$$, what is the minimum value of the function?

Accepted Answer

$$-6$$

Question 16

Which parameter in $$y = a \sin(bx + c) + d$$ affects the frequency of the function?

Accepted Answer

$$b$$

Question 17

A medical device records oscillations modeled by $$y = 0.8 \sin(5x). $$How many complete cycles does the function make from $$x = 0 to$$ $$x = 2\pi$$?

Accepted Answer

$$5$$

Question 18

Which of the following is the parent function for all sine transformations?

Accepted Answer

$$y = \sin(x)$$

Question 19

If $$y = 2 \sin(3x) + 4$$, what is the range of the function?

Accepted Answer

$$[2, 6]$$

Question 20

A pendulum swings such that its displacement is modeled by $$y = 6 \cos(x). $$What is the maximum displacement?

Accepted Answer

$$6$$

section 4.4

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드