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

$$x \u003e 13.33$$

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

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