Question 1

Which of the following graphs does NOT represent a function?

Accepted Answer

The graph of $y^2 = x$

Question 2

According to the vertical line test, which statement is true?

Accepted Answer

If any vertical line intersects a graph in more than one point, the graph does not define $y$ as a function of $x$.

Question 3

Given the function $f(x) = -2x + 7$, what is the $x$-intercept?

Accepted Answer

$x = 3.5$

Question 4

Given the function $f(x) = -2x + 7$, what is the $y$-intercept?

Accepted Answer

$y = 7$

Question 5

Which of the following is the correct interval notation for the domain of the function $f(x) = \sqrt{x}$?

Accepted Answer

$[0, \infty)$

Question 6

A graph passes through the points $(-2, 0)$, $(0, 2)$, and $(2, 0)$. What are the $x$-intercepts?

Accepted Answer

$x = -2$ and $x = 2$

Question 7

If a function's graph has arrows pointing left and right without bound, what is the domain?

Accepted Answer

$(-\infty, \infty)$

Question 8

Given the graph of $y = |x|$, what is the range of the function?

Accepted Answer

$[0, \infty)$

Question 9

Suppose a function $f$ is defined by the graph below. The graph passes through $(0, 3)$ and $(2, 0)$. What is the $y$-intercept?

Accepted Answer

$y = 3$

Question 10

A function $f$ is defined for all real numbers except $x = 2$. Which of the following is the correct interval notation for its domain?

Accepted Answer

$(-\infty, 2) \cup (2, \infty)$

Question 11

Given the graph of a function, how do you find the $x$-intercepts?

Accepted Answer

Solve $f(x) = 0$

Question 12

If a function $f$ has a domain of $(-\infty, 4]$, which of the following is true?

Accepted Answer

The function is defined for all $x \leq 4$

Question 13

A function $f$ is graphed and the highest point on the graph is at $(2, 5)$. What is the maximum value of $f$?

Accepted Answer

$5$

Question 14

Given the function $f(x) = x^2 - 4$, what are the $x$-intercepts?

Accepted Answer

$x = -2$ and $x = 2$

Question 15

If the graph of a function passes the vertical line test, which of the following must be true?

Accepted Answer

Each $x$-value corresponds to exactly one $y$-value

Question 16

A function $f$ is defined by $f(x) = \sqrt{x-1}$. What is the domain of $f$?

Accepted Answer

$[1, \infty)$

Question 17

Suppose a function $f$ is graphed and $f(-2) = 3$. What does this mean?

Accepted Answer

The point $(-2, 3)$ is on the graph of $f$

Question 18

If a function $f$ has a range of $(-\infty, 2]$, which of the following is true?

Accepted Answer

The largest value $f(x)$ can take is $2$

Question 19

Given the function $f(x) = |x|$, for what values of $x$ is $f(x) < 2$?

Accepted Answer

$-2 < x < 2$

Question 20

A real-world scenario: The height $h$ (in meters) of a ball thrown upward is given by $h(t) = -5t^2 + 20t + 1$, where $t$ is time in seconds. What is the $y$-intercept of this function?

Accepted Answer

$h = 1$

Graphs of Functions: Domain, Range, and Intercepts

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