Question 1

Which of the following is the correct domain of the function $f(x) = \sqrt{x-3}$?

Accepted Answer

$[3, \infty)$

Question 2

Find all values of $x$ satisfying the following conditions: $y = \frac{x^2}{2}$, $y = x + 2$, and $y = -1$, $y = 1$.

Accepted Answer

$x = -2$

Question 3

Simplify and write in the form $a + bi$: $\frac{6}{1 - 2i}$

Accepted Answer

$\frac{6}{1 - 2i} = \frac{6 + 12i}{5}$

Question 4

Solve the quadratic equation $2x^2 - 3x + 4 = 0$. Which of the following is a solution?

Question 5

Find the sum of the solutions to the quadratic equation $2x^2 - 10x = 50$.

Accepted Answer

$10$

Question 6

Given $f(x) = x^2 - 7x + 43$ and $g(x) = 2x^2 + 7x + 53$, find $g(x) - f(x)$.

Accepted Answer

$g(x) - f(x) = 2x^2 + 7x + 53 - (x^2 - 7x + 43) = x^2 + 14x + 10$

Question 7

Which of the following functions is odd?

Accepted Answer

$f(x) = x^3 - 7x$

Question 8

Find the inverse of $f(x) = \frac{2x - 3}{4}$.

Accepted Answer

$f^{-1}(x) = \frac{4x + 3}{2}$

Question 9

How can the graph $y = 2|x - 4| - 5$ be obtained from the graph $y = |x|$?

Accepted Answer

Stretched by factor 2 then shifted right 4 units and down 5 units.

Question 10

Find the equation of the line containing the point $(2, -3)$ and parallel to the line $2x - y = 5$.

Accepted Answer

$y = 2x - 7$

Question 11

If $f(x) = x^2 + 2x + 3$ and $g(x) = x^2 - 3x + 5$, find $f(x) + g(x)$.

Accepted Answer

$2x^2 - x + 8$

Question 12

Find the solution of the equation $9 - \sqrt{2x - 3} = 5x$.

Accepted Answer

$x = 6$

Question 13

Given $f(x) = x^2 - 7x + 43$, find $f(-7)$.

Accepted Answer

$172$

Question 14

For $f(x) = 2x^2 + x + 1$ and $g(x) = x - 1$, find $f(g(2))$.

Accepted Answer

$9$

Question 15

Find the equation of the line passing through $(2,5)$ and $(-4,3)$.

Accepted Answer

$y = \frac{1}{3}x + \frac{17}{3}$

Question 16

Find all values of $x$ satisfying the following conditions: $y = 2x$, $x = 2y$, and $y + y = 1$.

Accepted Answer

$x = \frac{1}{2}$

Question 17

Find the sum of the solutions to the equation $x^2 - 10x + 9 = 0$.

Accepted Answer

$10$

Question 18

Which of the following is the correct solution to $\sqrt{9 - 2x} = \sqrt{2x - 3}$?

Accepted Answer

$x = 6$

Question 19

Find the equation of the line containing the point $(2, -3)$ and parallel to the line $2x - y = 5$.

Accepted Answer

$y = 2x - 7$

College Algebra: Practice Questions and Key Concepts

Study Guide - Practice Questions