Question 1

Which of the following best describes the symmetry of the function $f(x) = \sin x$?

Accepted Answer

It is symmetrical about the origin (odd function).

Question 2

What is the amplitude of the function $f(x) = 3 \cos x$?

Accepted Answer

$3$

Question 3

Given the function $f(x) = \sin(x - \frac{\pi}{2})$, what transformation has occurred compared to $f(x) = \sin x$?

Accepted Answer

A horizontal shift right by $\frac{\pi}{2}$ units.

Question 4

What is the period of the function $f(x) = \cos(2x)$?

Accepted Answer

$\pi$

Question 5

Which of the following is the correct range for $f(x) = \sin x$?

Accepted Answer

$[-1, 1]$

Question 6

A sound wave can be modeled by $y = 2 \sin(3x)$. What is the amplitude and period of this wave?

Accepted Answer

Amplitude: $2$, Period: $\frac{2\pi}{3}$

Question 7

Which equation represents a cosine function that has been reflected over the x-axis and shifted up by 4 units?

Accepted Answer

$y = -\cos x + 4$

Question 8

If $f(x) = \sin x$ and $g(x) = \cos x$, which statement is true about their graphs?

Accepted Answer

The graph of $g(x)$ is a horizontal shift of $f(x)$ to the left by $\frac{\pi}{2}$.

Question 9

Which of the following functions is even?

Accepted Answer

$f(x) = \cos x$

Question 10

A Ferris wheel rotates such that the height of a passenger above the ground can be modeled by $h(t) = 10 + 5 \sin(\frac{\pi}{6} t)$, where $t$ is time in seconds. What is the maximum height reached?

Accepted Answer

$15$ meters

Question 11

Which transformation is applied to $y = \sin x$ to obtain $y = \sin(x) + 2$?

Accepted Answer

Vertical shift up by 2 units.

Question 12

What is the x-intercept of the function $f(x) = \cos x$ in the interval $[0, 2\pi]$?

Accepted Answer

$x = \frac{\pi}{2}$ and $x = \frac{3\pi}{2}$

Question 13

Which of the following best describes the domain of $f(x) = \sin x$?

Accepted Answer

$(-\infty, \infty)$

Question 14

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

Accepted Answer

Phase shift: $\pi$ left, Amplitude: $2$

Question 15

Which function has a period of $4\pi$?

Accepted Answer

$f(x) = \sin(\frac{x}{2})$

Question 16

A medical device uses a signal modeled by $y = 0.5 \cos(\pi t)$. What is the period of the signal?

Accepted Answer

$1$

Question 17

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

Accepted Answer

It passes through the origin and has a maximum at $x = \frac{\pi}{2}$.

Question 18

Which equation represents a sine function with amplitude $4$, period $\pi$, and phase shift $\frac{\pi}{4}$ to the right?

Accepted Answer

$y = 4 \sin(2x - \frac{\pi}{4})$

Question 19

Which of the following statements is true about the function $f(x) = \cos x$?

Accepted Answer

It is an even function.

Graphing Sine and Cosine Functions: Attributes, Symmetry, and Transformations

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