Question 1

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

Accepted Answer

$$x \geq -2$$

Question 2

Given the function $$R(x) = \frac{100x}{b + x}$$, if $$b = 20$$ and $$x = 60$$, what is the value of $$R(x)$$?

Accepted Answer

$$R(x) = 75$$

Question 3

Which of the following is NOT a polynomial function?

Accepted Answer

$$f(x) = \frac{1}{x}$$

Question 4

If $$f(x) = x^2$ + 4x + 3$$, what is $$f(a-2)$$?

Accepted Answer

$$a^2 - 1$

Question 5

Which of the following intervals represents all $$x$$ such that $$-1 \u003c x \u003c 4$$?

Accepted Answer

$$(-1, 4)$$

Question 6

The vertical line test is used to determine if a graph represents a function. Which statement is correct?

Accepted Answer

A graph is a function if every vertical line intersects it at most once.

Question 7

What is the zero of the function $$f(x) = x^2$ - 5x + 6$$?

Accepted Answer

$$x = 2$$ and $$x = 3$$

Question 8

Which of the following is the correct composition $$(f \circ g)(x) if$$ $$f(x) = x^2$ and g(x) = x + 1$?

Accepted Answer

$$(f \circ g)(x) = (x + 1)^2$

Question 9

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

Accepted Answer

$$x \in \mathbb{R} \setminus \{2, -2\}$$

Question 10

A rectangular corral with two partitions has outside dimensions $$x$$ and $$y$$ and a total area of $$2500$$ square feet. Which equation expresses this fact?

Accepted Answer

$$xy = 2500$$

Question 11

Which of the following is an example of a rational function?

Accepted Answer

$$f(x) = \frac{x^2$ + 1}{x - 3}$$

Question 12

Given $$f(x) = |x|$$, which statement is true?

Accepted Answer

$$f(x) is $$equal to $$-x$$ for $$x \u003c 0$$

Question 13

Which of the following is the correct solution to the quadratic equation $$x^2 - 4x + 3 = 0$?

Accepted Answer

$$x = 1$$ and $$x = 3$$

Question 14

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

Accepted Answer

$$x^2 + 2x$

Question 15

Which of the following is the correct expression for the surface area $$S of an $$open-top box with dimensions $$x$$, $$y$$, and $$z$$?

Accepted Answer

$$S = 2yz + 2xz + xy$$

Question 16

Which of the following is a power function?

Accepted Answer

$$f(x) = x^n$$ where $$n is a $$constant$

Question 17

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

Accepted Answer

$$(f \circ g)(x) = (x + 2)^2$

Question 18

Which of the following is the correct solution for $$x in $$the equation $$2x^3$$ - $$10x^2 + 12x = 0$?

Accepted Answer

$$x = 0, x = 2, x = 3$$

Business Calculus Study Notes: Functions and Their Properties

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