Question 1

Which of the following best describes a function $f: X \rightarrow Y$?

Accepted Answer

A rule that assigns each element in $X$ to exactly one element in $Y$.

Question 2

Given the function $I(t) = 100(0.06)t$, what is the value of $I$ when $t = 5$?

Accepted Answer

$I = 100(0.06)(5) = 30$

Question 3

In the equation $y = x + 2$, which variable is the independent variable?

Accepted Answer

$x$

Question 4

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

Accepted Answer

$y^2 = x$

Question 5

What is the domain of the function $h(x) = \frac{1}{x-6}$?

Accepted Answer

$(-\infty, \infty) - \{6\}$

Question 6

Which of the following is true about the equality of two functions $f$ and $g$?

Accepted Answer

They are equal if their domains are equal and $f(x) = g(x)$ for all $x$ in the domain.

Question 7

Given $f(x) = x^2 + 5$, what is the domain of $f$?

Accepted Answer

$(-\infty, \infty)$

Question 8

Which of the following is a constant function?

Accepted Answer

$h(x) = 2$

Question 9

Which of the following is NOT a polynomial function?

Accepted Answer

$g(x) = \sqrt{x}$

Question 10

Which of the following is a rational function?

Accepted Answer

$g(x) = \frac{2x+3}{x}$

Question 11

Given the case-defined function $F(s)$:

$F(s) = \begin{cases} 1 & 	ext{if } -1 < s < 1 \ 0 & 	ext{if } 1 < s < 2 \ s-3 & 	ext{if } 2 < s < 8 \end{cases}$

What is $F(7)$?

Accepted Answer

$4$

Question 12

What is the domain of the absolute-value function $f(x) = |x|$?

Accepted Answer

$(-\infty, \infty)$

Question 13

If $f(x) = x^2$ and $g(x) = x + 1$, what is $(f + g)(x)$?

Accepted Answer

$x^2 + x + 1$

Question 14

If $f(x) = x^2$ and $g(x) = x + 1$, what is $(f \circ g)(x)$?

Accepted Answer

$(x + 1)^2$

Question 15

Which of the following is the correct composite function $(f \circ g)(x)$ if $f(x) = 2x - 1$ and $g(x) = x^2$?

Accepted Answer

$2x^2 - 1$

Question 16

Which of the following is the degree of the polynomial $f(x) = 6x^3 + 7$?

Accepted Answer

$3$

Question 17

Which of the following is the leading coefficient of $f(x) = 3x^2 - 8x + 9$?

Accepted Answer

$3$

Question 18

If $f(x) = x^2$ and $g(x) = x + 1$, what is $(f \cdot g)(x)$?

Accepted Answer

$x^2(x + 1)$

Question 19

Which of the following is NOT a rational function?

Accepted Answer

$g(x) = x^2 + 1$

Functions and Their Properties in College Algebra

Study Guide - Practice Questions