Q: Which of the following graphs represents a function?

A graph that passes the vertical line test everywhere.

Q: Find all real and non-real zeros of the polynomial $f(x) = x^4 + 3x^2 + 4x + 12$.

There are no real zeros; all zeros are non-real complex numbers.

Q: Given the function $y = 5 - x$, which of the following is true?

The graph is a straight line with slope $-1$ and $y$-intercept $5$.

Q: Which of the following best describes the graph of $y = x^2 + 2x - 6$?

A parabola opening upwards with vertex at $(-1, -7)$.

Question 1

Which of the following is the correct domain of the function $g(x) = \sqrt{6 - 2x}$?

Accepted Answer

$x \leq 3$

Question 2

Given the relation $\{(2, 5), (3, 6), (2, 7), (3, 8)\}$, is this relation a function?

Accepted Answer

No, because the $x$-values repeat with different $y$-values.

Question 3

For the function $f(x) = \frac{x-2}{x+3}$, which of the following describes its vertical asymptote?

Accepted Answer

$x = -3$

Question 4

Given the piecewise function $f(x) = \begin{cases} 3x + 5 & x < -1 \ x^2 - 4 & -1 \leq x \leq 3 \ 1 - 3x & 3 < x \end{cases}$, what is $f(5)$?

Accepted Answer

$-14$

Question 5

A salesperson earns a base pay of $130 per week plus a commission of $9$ for every item sold. Which equation models her weekly salary $S$ as a function of the number of items $n$ sold?

Accepted Answer

$S = 130 + 9n$

Question 6

Find the difference quotient $\frac{f(x+h) - f(x)}{h}$ for $f(x) = 2x^2 - 6$. Simplify your answer.

Accepted Answer

$4x + 2h$

Question 7

Which of the following graphs represents a function?

Accepted Answer

A graph that passes the vertical line test everywhere.

Question 8

Given the quadratic function $y = x^2 + 2x - 6$, what are the $x$-intercepts?

Accepted Answer

$x = -3, x = 2$

Question 9

Write the equation of a line passing through the points $(5, -2)$ and $(2, -2)$.

Accepted Answer

$y = -2$

Question 10

For the function $f(x) = (x + 4)^2 - 3$, what is the vertex of the graph?

Accepted Answer

$(-4, -3)$

Question 11

Given $f(x) = (x + 4)^2 - 3$, what is the axis of symmetry?

Accepted Answer

$x = -4$

Question 12

Find all real and non-real zeros of the polynomial $f(x) = x^4 + 3x^2 + 4x + 12$.

Accepted Answer

There are no real zeros; all zeros are non-real complex numbers.

Question 13

Given the graph of $y = f(x)$, which interval is $f$ increasing?

Accepted Answer

$(-\infty, -2)$

Question 14

Given $f(x) = x^2 + 2x - 6$, what is the axis of symmetry?

Accepted Answer

$x = -1$

Question 15

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

Accepted Answer

$g(x) = (x - 3)^2 + 3$

Question 16

Given the function $y = 5 - x$, which of the following is true?

Accepted Answer

The graph is a straight line with slope $-1$ and $y$-intercept $5$.

Question 17

For the quadratic $y = x^2 + 2x - 6$, what is the minimum value of the function?

Accepted Answer

$-7$

Question 18

Given the function $h(x) = 2x^2 - 2$, what is the $y$-intercept?

Accepted Answer

$-2$

Question 19

Which of the following best describes the graph of $y = x^2 + 2x - 6$?

Accepted Answer

A parabola opening upwards with vertex at $(-1, -7)$.

Question 20

If $R(p) = -6p^2 + 90p$ models the revenue $R$ as a function of the price $p$ in dollars of a product, what price maximizes the revenue?

Accepted Answer

$p = 7.5$

College Algebra: Functions, Graphs, and Applications Study Guide

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