Question 1

Suppose the revenue function for a company is given by $R(x) = 20x$ and the cost function is $C(x) = 5x + 100$. What is the break-even quantity?

Accepted Answer

$x = 10$

Question 2

Which of the following graphs passes the vertical line test and represents a function?

Accepted Answer

A graph where a vertical line never intersects the curve more than once.

Question 3

Given the function $f(x) = \sqrt{x-3}$, what is the domain of $f(x)$?

Accepted Answer

$x \geq 3$

Question 4

A rational function is given by $f(x) = \frac{2x^2 + 1}{x^2 - 4}$. What are the vertical asymptotes?

Accepted Answer

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

Question 5

For the function $f(x) = \frac{3x^2 + 5}{x^2 - 1}$, what is the horizontal asymptote?

Accepted Answer

$y = 3$

Question 6

Which of the following best describes the range of the function $f(x) = x^2 + 2$?

Accepted Answer

$y \geq 2$

Question 7

A company’s profit function is $P(x) = 15x - 200$. What is the minimum number of units $x$ that must be sold for the company to make a profit?

Accepted Answer

$x > 13.33$

Question 8

Given the system of equations: $2x + 3y = 7$ and $4x + 6y = 14$, what type of solution does this system have?

Accepted Answer

Infinitely many solutions (dependent)

Question 9

A rectangular lot is to be fenced on three sides with 200 meters of fencing, with one side formed by a brick wall. If the length of the wall is $l$ and the width is $w$, which equation represents the area $A$ as a function of $l$?

Accepted Answer

$A(l) = l\left(\frac{200 - l}{2}\right)$

Question 10

Which of the following is NOT a valid reason for a value to be excluded from the domain of a function?

Accepted Answer

The value makes the output negative.

Question 11

If the degree of the numerator of a rational function is less than the degree of the denominator, what is the horizontal asymptote?

Accepted Answer

$y = 0$

Question 12

Given $f(x) = \frac{5x^3 + 2}{2x^3 - 7}$, what is the horizontal asymptote?

Accepted Answer

$y = \frac{5}{2}$

Question 13

Which of the following best describes a consistent system of linear equations?

Accepted Answer

A system with at least one solution.

Question 14

Suppose $f(x) = \frac{1}{x-3}$. What is the domain of $f(x)$?

Accepted Answer

$x 
eq 3$

Question 15

If $f(x) = 2x + 5$, what is $f(4)$?

Accepted Answer

$13$

Question 16

Which of the following is the correct definition of the range of a function?

Accepted Answer

The set of all possible output values.

Question 17

Given the system $x + y = 5$ and $2x + 2y = 10$, what type of solution does this system have?

Accepted Answer

Infinitely many solutions

Question 18

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

Accepted Answer

$y \geq 0$

Question 19

Which of the following best describes a dependent system of equations?

Accepted Answer

The system has infinitely many solutions.

Question 20

If $f(x) = \frac{x^2 - 4}{x - 2}$, what is the domain of $f(x)$?

Accepted Answer

$x 
eq 2$

Business Calculus Study Notes: Nonlinear Functions, Domain & Range, Rational Functions, Asymptotes, and Linear Systems

Study Guide - Practice Questions

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