As $x \to \infty$, $f(x) \to -\infty$; as $x \to -\infty$, $f(x) \to \infty$

Question 1

Which of the following is the correct equation for a line passing through the points $(2, 3)$ and $(4, 7)$?

Accepted Answer

$y = 2x - 1$

Question 2

Given the function $f(x) = x^2 - 4x + 3$, what are the $x$-intercepts?

Accepted Answer

$x = 3$ and $x = 1$

Question 3

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

Accepted Answer

A V-shaped graph opening upwards

Question 4

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

Accepted Answer

$9$

Question 5

Which of the following intervals represents the domain of $f(x) = \frac{1}{x-2}$?

Accepted Answer

$(-\infty, 2) \cup (2, \infty)$

Question 6

A business’s profit function is $P(x) = -2x^2 + 8x + 10$. What is the maximum profit, and at what value of $x$ does it occur?

Accepted Answer

Maximum profit is $18$ at $x = 2$

Question 7

Which of the following is the correct inverse of the function $f(x) = 3x + 5$?

Accepted Answer

$f^{-1}(x) = \frac{x-5}{3}$

Question 8

Which of the following best describes the end behavior of $f(x) = -x^3 + 2x$?

Accepted Answer

As $x 	o \infty$, $f(x) 	o -\infty$; as $x 	o -\infty$, $f(x) 	o \infty$

Question 9

Which of the following is the correct equation for a circle centered at the origin with radius $5$?

Accepted Answer

$x^2 + y^2 = 25$

Question 10

If $f(x) = \frac{2x+1}{x-3}$, what is the vertical asymptote?

Accepted Answer

$x = 3$

Question 11

Which of the following is the correct solution to the system: $2x + y = 5$ and $x - y = 1$?

Accepted Answer

$(2, 1)$

Question 12

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

Accepted Answer

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

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 domain for $f(x) = \sqrt{x-2}$?

Accepted Answer

$[2, \infty)$

Question 15

A company’s cost function is $C(x) = 5x + 200$. What is the fixed cost?

Accepted Answer

$200$

Question 16

Which of the following is the correct solution for $x$ in $\ln(x) = 2$?

Accepted Answer

$x = e^2$

Question 17

Which of the following is the correct equation for a parabola opening upwards with vertex at $(0,0)$?

Accepted Answer

$y = x^2$

Question 18

If $f(x) = 2x^2 - 8x + 6$, what is the minimum value of $f(x)$?

Accepted Answer

$-2$

Question 19

Which of the following is the correct horizontal asymptote for $f(x) = \frac{3x^2 + 2}{x^2 - 1}$?

Accepted Answer

$y = 3$

Question 20

Which of the following is the correct solution to $e^{2x} = 7$?

Accepted Answer

$x = \frac{1}{2} \ln(7)$

Business Calculus: Functions, Graphs, and Models – Comprehensive Study Notes

Study Guide - Practice Questions