Question 1

Which of the following relations is a function?

Accepted Answer

$\{(2, 5), (0, 2), (3, 9)\}$

Question 2

Given the equation $y = -2x + 10$, rewrite it in function notation and evaluate $f(3)$.

Accepted Answer

$f(3) = -2 	imes 3 + 10 = 4$

Question 3

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

Accepted Answer

A graph of a parabola opening upwards

Question 4

What is the domain of the function $f(x) = \sqrt{x + 4}$? Express your answer in interval notation.

Accepted Answer

$[-4, \infty)$

Question 5

Find the domain of $f(x) = \dfrac{1}{x^2 - 5x + 6}$. Express your answer in interval notation.

Accepted Answer

$(-\infty, 2) \cup (2, 3) \cup (3, \infty)$

Question 6

Which of the following equations is NOT a function?

Accepted Answer

$x^2 + y^2 = 25$

Question 7

Given the graph of $f(x)$ with domain $[-4, 0) \cup [1, 4]$ and range $(-3, 1] \cup [1, 3]$, which of the following is true?

Accepted Answer

The function is not defined for $x$ between $0$ and $1$

Question 8

A chemical reaction's temperature $T$ (in $^\circ$C) is modeled by $T(t) = 5t + 20$, where $t$ is time in minutes. What is the temperature after 8 minutes?

Accepted Answer

$T(8) = 60$ $^\circ$C

Question 9

Which of the following statements about functions is correct?

Accepted Answer

A function assigns exactly one output to each input

Question 10

If $f(x) = \sqrt{x}$, what is the range of $f$?

Accepted Answer

$[0, \infty)$

Question 11

A hospital monitors a patient's heart rate $H(t)$, modeled by $H(t) = 70 + 5t$ for $0 \leq t \leq 10$. What is the domain of $H$?

Accepted Answer

$[0, 10]$

Question 12

Which interval notation correctly represents all real numbers except $x = 5$?

Accepted Answer

$(-\infty, 5) \cup (5, \infty)$

Question 13

Given $f(x) = \dfrac{1}{x-2}$, which value is NOT in the domain?

Accepted Answer

$x = 2$

Question 14

A relation is given by the set $\{(1, 2), (2, 3), (1, 4)\}$. Is this a function?

Accepted Answer

No, because input $1$ has two different outputs

Question 15

Which of the following is the correct set builder notation for the domain $[1, 5]$?

Accepted Answer

$\{x | 1 \leq x \leq 5\}$

Question 16

If $f(x) = x^2 - 4$, what is the range of $f$?

Accepted Answer

$[-4, \infty)$

Question 17

Which of the following equations will always pass the vertical line test?

Accepted Answer

$y = 2x + 1$

Question 18

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

Accepted Answer

$[1, \infty)$

Question 19

Which of the following is NOT a valid way to express the range of a function?

Accepted Answer

Using $x$ values only

Question 20

If $f(x) = \dfrac{1}{x^2}$, what is the domain of $f$?

Accepted Answer

$(-\infty, 0) \cup (0, \infty)$

Relations, Functions, Domain, and Range: College Algebra Study Notes

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