Question 1

Which of the following relations is NOT a function?

Accepted Answer

$$\{(2, 5), (0, 2), (2, 9)\}$$

Question 2

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

Accepted Answer

$$[0, \infty)$$

Question 3

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

Accepted Answer

A graph where every vertical line crosses the curve at most once

Question 4

What is the range of the function $$f(x) = x^2$?

Accepted Answer

$$[0, \infty)$$

Question 5

Given the piecewise function $$f(x) = \begin{cases} -x & x \u003c -1 \ x^2$ - 4 & x \geq -1 \end{cases}$$, what is $$f(-3)$$?

Accepted Answer

$$-(-3) = 3$$

Question 6

Which of the following describes the transformation $$g(x) = f(x-2) + 5$$?

Accepted Answer

Shift right 2 units, up 5 units

Question 7

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

Accepted Answer

$$(f+g)(x) = x^2$ + x + 1$$, domain: $$(-\infty, \infty)$$

Question 8

Simplify the expression $$(2x^4)(7x^2$)$ using exponent rules.

Accepted Answer

$$14x^6$$

Question 9

Which of the following is the correct application of the power rule for exponents: $$(a^3)^2$?

Accepted Answer

$$a^6$$

Question 10

Given $$f(x) = \sqrt{x+4} + 30$$ and $$g(x) = \sqrt{x+4} - 2x + 35$$, what is $$(f-g)(x)$$?

Accepted Answer

$$2x - 5 - 30 + 35$$

Question 11

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

Accepted Answer

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

Question 12

Which property of exponents is used to simplify $$\frac{a^7$}{a^3$}$$?

Accepted Answer

Quotient Rule: $$a^m / a^n = a$$^{m-n}$$

Question 13

Which of the following is the range of the function $$f(x) = \sqrt{x}$$?

Accepted Answer

$$[0, \infty)$$

Question 14

If $$f(x) is an $$even function, which of the following is true?

Accepted Answer

$$f(-x) = f(x)$$

Question 15

Which transformation is represented by $$-f(x)$$?

Accepted Answer

Reflection over the $$x-$$axis

Question 16

Given $$h(x) = 2x^3$ - 4$$ and $$k(x) = x^2$ + 2$$, what is $$(h \cdot k)(x)$$?

Accepted Answer

$$2x^5$$ - $$4x^2$$ + $$4x^3 - 8$

Question 17

Which of the following is the correct simplification of $$(x^2$$ $$y^7$$ / $$x^5$$ $$y^4$$)^{-1}$?

Accepted Answer

$$x^{-3}$$ $$y^{3}$$

Question 18

Which of the following is the correct domain for $$f(x) = \sqrt{x-3}$$?

Accepted Answer

$$[3, \infty)$$

Question 19

If $$f(x) is $$increasing on the interval $$(1, 4)$$, which of the following is true?

Accepted Answer

$$f(x_2$) \u003e f(x_1$)$$ for $$x_2$$ \u003e $$x_1 in$$ $$(1, 4)$

Business Calculus: Functions, Exponents, and Logarithms – Mini-Textbook Study Notes

Study Guide - Practice Questions