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

Study Guide - Practice Questions

Study Guide - Flashcards