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

Accepted Answer

$2\pi$

Question 3

Given the function $f(x) = 3\sin(x - \frac{\pi}{2})$, what is the amplitude?

Accepted Answer

$3$

Question 4

Which transformation occurs when you change $f(x) = \sin x$ to $f(x) = \sin(x + \frac{\pi}{4})$?

Accepted Answer

Horizontal shift left by $\frac{\pi}{4}$

Question 5

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

Accepted Answer

$[-1, 1]$

Question 6

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

Accepted Answer

$f(x)$ has y-intercept $0$ and $g(x)$ has y-intercept $1$

Question 7

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

Accepted Answer

$\frac{2\pi}{3}$

Question 8

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

Accepted Answer

$f(-x) = f(x)$, so it is even.

Question 9

Given $f(x) = \sin x$, what are the x-intercepts within one period?

Accepted Answer

$0, \pi, 2\pi$

Question 10

A Ferris wheel rotates such that the height of a seat above the ground is 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

$15$

Question 11

Which equation represents a cosine function with amplitude $2$, period $\pi$, and phase shift right $\frac{\pi}{4}$?

Accepted Answer

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

Question 12

If $y = \sin x$ is transformed to $y = -\sin x$, what happens to the graph?

Accepted Answer

It is reflected over the x-axis.

Question 13

Which of the following functions is neither even nor odd?

Accepted Answer

$f(x) = x + 1$

Question 14

A medical device uses $y = 4\cos(\frac{\pi}{2}t)$ to model a periodic signal. What is the amplitude and period?

Accepted Answer

Amplitude $4$, period $4$

Question 15

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

Accepted Answer

$(-\infty, \infty)$

Question 16

If $y = \sin(x)$ is shifted up by 2 units and stretched vertically by a factor of 3, what is the new equation?

Accepted Answer

$y = 3\sin(x) + 2$

Question 17

Which of the following is the parent function for all sinusoidal graphs?

Accepted Answer

$y = \sin x$

Question 18

A chemical reaction oscillates according to $C(t) = 2\sin(\pi t)$. How many complete cycles occur between $t = 0$ and $t = 2$?

Accepted Answer

2

Question 19

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

Accepted Answer

It starts at $y = 1$ when $x = 0$

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

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