Q: Which of the following is the correct definition of a function?

A rule that assigns to each element in the domain exactly one element in the codomain.

Q: If $f(x) = x^2$ and $g(x) = x + 1$, what is the domain of $\frac{f(x)}{g(x)}$?

All real numbers except $x = -1$

Question 1

A bank offers a simple interest rate of 6% per year. If you invest $100, the interest earned after $t$ years is given by $I = 100(0.06)t$. What is the value of $I$ after 5 years?

Accepted Answer

$I = 30$

Question 2

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

Accepted Answer

$y^2 = x$

Question 3

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

Accepted Answer

All real numbers except $x = 6$

Question 4

Which of the following is a constant function?

Accepted Answer

$h(x) = 2$

Question 5

Which of the following is NOT a polynomial function?

Accepted Answer

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

Question 6

Suppose $f(x) = x^2$ and $g(x) = x + 1$. What is $(f + g)(x)$?

Accepted Answer

$x^2 + x + 1$

Question 7

Given $f(x) = x^2$ and $g(x) = x + 1$, what is the composite function $(f \circ g)(x)$?

Accepted Answer

$(f \circ g)(x) = (x + 1)^2$

Question 8

Which of the following is a rational function?

Accepted Answer

$f(x) = \frac{2x + 3}{x - 1}$

Question 9

The absolute-value function $f(x) = |x|$ has which domain?

Accepted Answer

All real numbers

Question 10

A case-defined function $F(s)$ is given by $F(s) = 1$ if $-1 < s < 1$, $F(s) = 0$ if $1 < s < 2$, and $F(s) = s - 3$ if $2 < s < 8$. What is $F(7)$?

Accepted Answer

$F(7) = 4$

Question 11

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

Accepted Answer

2

Question 12

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

Accepted Answer

$x^2(x + 1)$

Question 13

Which of the following is the correct definition of a function?

Accepted Answer

A rule that assigns to each element in the domain exactly one element in the codomain.

Question 14

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

Accepted Answer

$x^2 - x - 1$

Question 15

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

Accepted Answer

All real numbers except $x = -1$

Question 16

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

Accepted Answer

6

Question 17

Which of the following is the zero function?

Accepted Answer

$f(x) = 0$

Question 18

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

Accepted Answer

$\frac{x^2}{x + 1}$

Question 19

Which of the following is the correct composite function for $f(x) = (2x - 1)^2$ expressed as $f(x) = h(g(x))$ where $g(x) = 2x - 1$ and $h(x) = x^2$?

Accepted Answer

$f(x) = h(g(x)) = (2x - 1)^2$

Question 20

Which of the following is the domain of the function $f(x) = \sqrt{x - 2}$?

Accepted Answer

All real numbers $x \geq 2$

Functions and Their Properties in College Algebra

Study Guide - Practice Questions

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