A V-shaped graph opening upwards

Question 1

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

Accepted Answer

$[2, \infty)$

Question 2

Given the graph of a function that passes through the points $(-2, 0)$, $(0, 2)$, and $(2, 0)$, which of the following could be its equation?

Accepted Answer

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

Question 3

Which of the following intervals represents the range of the function $f(x) = x^2 - 4$?

Accepted Answer

$[-4, \infty)$

Question 4

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

Accepted Answer

$f(g(2)) = 2 \cdot 4 + 3 = 11$

Question 5

Which of the following is the solution set for $|x - 3| < 5$?

Accepted Answer

$(-2, 8)$

Question 6

A quadratic function $f(x)$ has its vertex at $(1, -4)$ and passes through the point $(0, 0)$. Which of the following could be its equation?

Accepted Answer

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

Question 7

Which of the following represents the solution to $\sqrt{x+1} = 3$?

Accepted Answer

$x = 8$

Question 8

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

Accepted Answer

$f(2) + g(2) = 4 + 3 = 7$

Question 9

Which of the following is the correct interval notation for the set $\{x | x \geq -3 \}$?

Accepted Answer

$[-3, \infty)$

Question 10

Given the function $f(x) = |x|$, which of the following statements is true?

Accepted Answer

The function is even.

Question 11

Solve for $x$: $2x - 5 = 9$

Accepted Answer

$x = 7$

Question 12

Which of the following is the solution set for $x^2 - 4 = 0$?

Accepted Answer

$\{2, -2\}$

Question 13

If $f(x) = x^2 - 2x + 1$, what is the vertex of the parabola?

Accepted Answer

$(1, 0)$

Question 14

Which of the following is the correct solution to $|2x + 1| = 7$?

Accepted Answer

$x = 3, x = -4$

Question 15

Which of the following is the inverse of the function $f(x) = 2x + 5$?

Accepted Answer

$f^{-1}(x) = \frac{x-5}{2}$

Question 16

If $f(x) = x^2$ and $g(x) = \sqrt{x}$, what is $(f \circ g)(4)$?

Accepted Answer

$f(g(4)) = (\sqrt{4})^2 = 4$

Question 17

Which of the following is the solution set for $x^2 + 1 = 0$?

Accepted Answer

$\{i, -i\}$

Question 18

Which of the following best describes the graph of $y = |x|$?

Accepted Answer

A V-shaped graph opening upwards

Question 19

If $f(x) = x^2 - 4x + 3$, for which value of $x$ does $f(x) = 0$?

Accepted Answer

$x = 1$ or $x = 3$

Question 20

Which of the following is the correct interval notation for the set $\{x | x < 5\}$?

Accepted Answer

$(-\infty, 5)$

Chapter 1 Review: Equations, Inequalities, and Graphs

Study Guide - Practice Questions