Question 1

Which of the following sets of ordered pairs represents a function?

Accepted Answer

$\{(2,5), (3,6), (4,7)\}$

Question 2

Given the equation $y = x^2 + 3$, which of the following statements is true?

Accepted Answer

It represents a function because each $x$ value has exactly one $y$ value.

Question 3

What is the domain of the function $f(x) = \frac{1}{x-2}$?

Accepted Answer

$x 
eq 2$

Question 4

A medical researcher models the temperature $T$ (in °C) of a patient over time $t$ (in hours) with $T(t) = 37 + 0.5t$. What is the range of $T$ if $t$ is between 0 and 4?

Accepted Answer

$[37, 39]$

Question 5

Which graph passes the vertical line test and therefore represents a function?

Accepted Answer

A parabola opening upwards

Question 6

Given the function $f(x) = 2x - 5$, what is $f(3)$?

Accepted Answer

$6 - 5 = 1$

Question 7

Which of the following equations does NOT represent $y$ as a function of $x$?

Accepted Answer

$x = y^2$

Question 8

A chemical reaction is modeled by $C(t) = 5e^{-0.2t}$, where $C$ is the concentration at time $t$. What is the domain of $C$?

Accepted Answer

$t \geq 0$

Question 9

If the graph of a relation fails the vertical line test, what does this indicate?

Accepted Answer

The relation is not a function.

Question 10

Given the function $f(x) = \sqrt{x-1}$, what is the domain?

Accepted Answer

$x \geq 1$

Question 11

A population of bacteria is modeled by $P(t) = 1000 \cdot 2^t$. What is the value of $P(3)$?

Accepted Answer

$8000$

Question 12

Which of the following is the range of the function $f(x) = x^2$ for $x$ in $[-2, 3]$?

Accepted Answer

$[0, 9]$

Question 13

A function $f$ is defined by $f(x) = \frac{2x+1}{x-3}$. What is the domain of $f$?

Accepted Answer

$x 
eq 3$

Question 14

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

Accepted Answer

The range is $y \geq 0$

Question 15

A function $g$ is graphed and passes through the points $(0,2)$, $(1,4)$, $(2,8)$, $(3,16)$. What is $g(2)$?

Accepted Answer

$8$

Question 16

Which of the following is NOT a function?

Accepted Answer

$x^2 + y^2 = 1$

Question 17

If $f(x) = 3x - 2$ and $g(x) = x^2$, what is $f(g(2))$?

Accepted Answer

$10$

Question 18

A function $h$ is defined by $h(x) = \frac{1}{x}$ for $x 
eq 0$. What is the range of $h$?

Accepted Answer

$y 
eq 0$

Question 19

Which of the following describes the range of the function $f(x) = 2x + 1$ for $x$ in $[0, 5]$?

Accepted Answer

$[1, 11]$

Question 20

A function $f$ is graphed and you observe that for some $x$ values, there are two $y$ values. What does this indicate?

Accepted Answer

The graph does not represent a function.

Relations and Functions: Domain, Range, and Graphical Analysis

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