Question 1

Which of the following relations is NOT a function?

Accepted Answer

A relation where some $$x-$$values are paired with more than one $$y-$$value.

Question 2

Given the function $$f(x) = \dfrac{3x-10}{x-5}$$, what is the domain of $$f in $$set notation?

Accepted Answer

$$\{x|x 
eq 5\}$$

Question 3

Which interval notation correctly represents all real numbers except $$x = -2$$?

Accepted Answer

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

Question 4

A function $$f is $$defined as $$f(x) = \sqrt{x-3}. $$What is the domain of $$f in $$interval notation?

Accepted Answer

$$[3, \infty)$$

Question 5

Which of the following statements about the vertical line test is TRUE?

Accepted Answer

If a vertical line crosses a graph at only one point everywhere, the relation is a function.

Question 6

Given $$f(x) = x^2$ - 4x + 3$$, what is $$f(5)$$?

Accepted Answer

$$8$$

Question 7

Which of the following is the correct difference quotient for $$f(x) = 2x^2$ - 3x$$?

Accepted Answer

$$\dfrac{2(x+h)^2$ - 3(x+h) - [2x^2$ - 3x]}{h}$$

Question 8

If $$f(x) is an $$even function, which of the following must be true for all $$x in $$the domain?

Accepted Answer

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

Question 9

Suppose $$g(x) is a $$piecewise function defined as $$g(x) = \begin{cases} x+2 & 	ext{if } x \u003c 0 \ 3x & 	ext{if } x \geq 0 \end{cases}. $$What is $$g(-3)$$?

Accepted Answer

$$-1$$

Question 10

Which transformation occurs when the parent function $$f(x) = x^2$ is changed to f(x$$) = $$(x-4)^2 + 2$?

Accepted Answer

Shift right 4 units and up 2 units

Question 11

Given $$f(x) = \dfrac{x+1}{x^2$+4x-5}$$, what values must be excluded from the domain?

Accepted Answer

$$x = -5$$ and $$x = 1$$

Question 12

Which of the following best describes the end behavior of $$f(x) = -2x^3$ + 5x as$$ $$x 	o \infty$$?

Accepted Answer

$$f(x) 	o -\infty$$

Question 13

A function $$h(x) is $$defined as $$h(x) = \dfrac{4}{x}. $$What is the domain of $$h in $$set notation?

Accepted Answer

$$\{x|x 
eq 0\}$$

Question 14

Which of the following is NOT a property of odd functions?

Accepted Answer

Their graphs are symmetric with respect to the $$y-$$axis.

Question 15

Given $$f(x) = \sqrt{4 - 3x}$$, what is the domain of $$f in $$interval notation?

Accepted Answer

$$(-\infty, \dfrac{4}{3}]$$

Question 16

If $$f(x) = x^2$ and g(x) = 2x + 1$, what is (f+g)(3$$)$$?

Accepted Answer

$$16$$

Question 17

Which of the following is the correct set notation for the range of $$f(x) = x^2$?

Accepted Answer

$$\{y|y \geq 0\}$$

Question 18

A hospital monitors the temperature of a patient every hour. The temperature readings are plotted as points on a graph. Which statement is TRUE about the relation?

Accepted Answer

The relation is a function because each time corresponds to exactly one temperature.

Question 19

Given $$f(x) = x^2$ - x$$ and $$h(x) = 2x + 7$$, what is $$(f \cdot h)(2)$$?

Accepted Answer

$$10$$

Functions and Their Graphs: Precalculus Study Guide

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