$[\text{minimum value}, \infty)$

Question 1

Which of the following equations is NOT a function when graphed in the Cartesian plane?

Accepted Answer

$x^2 + y^2 = 4$

Question 2

Given the quadratic equation $3x^2 + 6x - 9 = 0$, what are the solutions for $x$?

Accepted Answer

$x = \dfrac{-6 \pm \sqrt{144}}{6}$

Question 3

Which of the following describes the domain of the function $f(x) = \sqrt{x-5}$?

Accepted Answer

$x \geq 5$

Question 4

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

Accepted Answer

$x^2 + x + 1$

Question 5

Which of the following is the correct factorization of $x^2 - 9$?

Accepted Answer

$(x - 3)(x + 3)$

Question 6

The graph of $y = f(x)$ is reflected about the $x$-axis. Which equation represents the new graph?

Accepted Answer

$y = -f(x)$

Question 7

What is the range of the function $f(x) = 2x^2 - 5x + 2$?

Accepted Answer

$[	ext{minimum value}, \infty)$

Question 8

Which of the following is the correct binomial expansion for $(x + a)^2$?

Accepted Answer

$x^2 + 2xa + a^2$

Question 9

Given $f(x) = x^3$ and $g(x) = x - 2$, what is the composite function $(f \circ g)(x)$?

Accepted Answer

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

Question 10

Which of the following is true about the exponential function $f(x) = a^x$ where $a > 0$?

Accepted Answer

The range is $(0, \infty)$

Question 11

If $f(x)$ is an even function, which of the following must be true?

Accepted Answer

$f(-x) = f(x)$

Question 12

Which of the following is the correct factorization for $x^3 + a^3$?

Accepted Answer

$(x + a)(x^2 - ax + a^2)$

Question 13

A function $f(x)$ is defined as $f(x) = |x|$. Which of the following statements is true?

Accepted Answer

$f(x)$ is even

Question 14

Which transformation will shift the graph of $y = f(x)$ three units to the right?

Accepted Answer

$y = f(x - 3)$

Question 15

Given the function $f(x) = \frac{1}{x - 2}$, what is the domain?

Accepted Answer

$x 
eq 2$

Question 16

Which of the following is the correct factorization for $x^2 + 2x + 1$?

Accepted Answer

$(x + 1)^2$

Question 17

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

Accepted Answer

$2x^3$

Question 18

Which of the following is the correct formula for the quadratic formula?

Accepted Answer

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Question 19

Which of the following is the correct expansion for $(x - a)^3$?

Accepted Answer

$x^3 - 3x^2a + 3xa^2 - a^3$

Question 20

Which of the following statements about the Cartesian plane is correct?

Accepted Answer

The origin is the point $(0, 0)$ where the $x$-axis and $y$-axis intersect.

Algebraic Foundations: Special Products, Factorization, and Functions

Study Guide - Practice Questions