Question 1

Which of the following relations is a function?

Accepted Answer

The set $$\{(-3, 5), (0, 2), (3, 5)\}$$

Question 2

Given the function $$f(x) = \sqrt{x-2}$$, what is the domain of $$f in $$interval notation?

Accepted Answer

$$[2, \infty)$$

Question 3

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

Accepted Answer

A parabola opening upwards

Question 4

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

Accepted Answer

$$[0, \infty)$$

Question 5

Given the piecewise function $$f(x) = \begin{cases} 2x+4 & x \u003c 0 \ x^2$ & 0 \leq x \u003c 2 \ x^3$+5 & x \geq 2 \end{cases}$$, what is $$f(5)$$?

Accepted Answer

$$5^3 + 5 = 130$

Question 6

Which of the following describes the transformation $$g(x) = f(x-3) + 2$$?

Accepted Answer

Shift right 3 units, up 2 units

Question 7

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

Accepted Answer

$$(-\infty, \infty)$$

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 $$(a^m)^n = a$$^{mn}$$?

Accepted Answer

$$(x^2)^3$ = x^6$

Question 10

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

Accepted Answer

$$[-4, \infty)$$

Question 11

Which of the following is NOT a property of logarithms?

Accepted Answer

$$\log_b(x+y) = \log_b x + \log_b y$$

Question 12

Which of the following is the correct change of base formula for $$\log_2$ 7$$?

Accepted Answer

$$\frac{\log 7}{\log 2}$$

Question 13

Which of the following best describes the domain of the logarithmic function $$f(x) = \log_b(x-3)$$?

Accepted Answer

$$(3, \infty)$$

Question 14

If $$f(x) = x^3$ and g(x$$) = $$x^2$$, what is $$(f \cdot g)(x)$$?

Accepted Answer

$$x^5$$

Question 15

Which of the following is the correct interval notation for the set $$\{x | -4 \leq x \u003c 5\}$$?

Accepted Answer

$$[-4, 5)$$

Question 16

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

Accepted Answer

Reflection over the $$x-$$axis

Question 17

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

Accepted Answer

$$[0, \infty)$$

Question 19

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

Accepted Answer

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

Functions and Graphs: Foundations for Business Calculus

Study Guide - Practice Questions