Question 1

Which of the following best describes the graph of the function $f(x) = |x|$?

Accepted Answer

A V-shaped graph opening upwards with vertex at $(0,0)$

Question 2

Given the quadratic function $f(x) = -x^2 + 4x + 5$, what is the maximum value of $f(x)$?

Accepted Answer

$9$

Question 3

If $f(x) = x^2 - 4$, what are the $x$-intercepts of the graph?

Accepted Answer

$x = -2$ and $x = 2$

Question 4

Which of the following is the correct solution set for $x^2 = 9$?

Accepted Answer

$\{ -3, 3 \}$

Question 5

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

Accepted Answer

$[2, \infty)$

Question 6

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

Accepted Answer

$9$

Question 7

Which of the following represents the solution to $x^2 - 5x + 6 = 0$?

Accepted Answer

$x = 2$ and $x = 3$

Question 8

Which of the following is the correct vertex of the parabola $y = x^2 - 6x + 8$?

Accepted Answer

$(3, -1)$

Question 9

If $f(x) = \sqrt{9 - x^2}$, what is the range of $f(x)$?

Accepted Answer

$[0, 3]$

Question 10

Which of the following is the correct factorization of $x^2 - 4x + 4$?

Accepted Answer

$(x - 2)^2$

Question 11

A business finds its profit $P(x)$ in thousands of dollars is given by $P(x) = -2x^2 + 8x - 3$, where $x$ is the number of units sold in hundreds. What is the maximum profit?

Accepted Answer

$5$ thousand dollars

Question 12

Which of the following is the correct solution to $\sqrt{x} = 5$?

Accepted Answer

$x = 25$

Question 13

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

Accepted Answer

$36$

Question 14

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

Accepted Answer

$\{ i, -i \}$

Question 15

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

Accepted Answer

$0$

Question 16

Which of the following is the correct solution to $x^2 = 0$?

Accepted Answer

$x = 0$

Question 17

If $f(x) = x^2 + 2x + 1$, what is the $y$-intercept of the graph?

Accepted Answer

$1$

Question 18

Which of the following is the correct solution to $x^2 - 16 = 0$?

Accepted Answer

$x = -4$ and $x = 4$

Question 19

If $f(x) = \sqrt{x}$, what is the domain of $f(x)$?

Accepted Answer

$[0, \infty)$

Question 20

Which of the following is the correct solution to $x^2 + 4x + 4 = 0$?

Accepted Answer

$x = -2$

Fundamental Concepts in Business Calculus: Functions, Graphs, and Algebraic Operations

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