Question 1

Which of the following best defines a function?

Accepted Answer

A rule that assigns to each element in a set D a unique value in a set R.

Question 2

Given the mapping diagram below, does it represent a function?

-2 → 5
-1 → 6
0 → 7
1 → 8
2 → 6

Accepted Answer

Yes, because each element in the domain is paired with exactly one element in the range.

Question 3

Given the set of points $$\{(-3,2), (0,3), (1,5), (0,-2), (6,6)\}$$, does this relation represent a function?

Accepted Answer

No, because the input $$x=0 is $$paired with two different outputs.

Question 4

What is the domain of the function $$g(x) = \frac{4}{x-2}$$?

Accepted Answer

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

Question 5

Given $$f(x) = x^2$ - 3x$$ and $$g(x) = \frac{1}{x}$$, what is $$(g \circ f)(x)$$?

Accepted Answer

$$\frac{1}{x^2$ - 3x}$$

Question 6

For the composite function $$h(x) = \sqrt{9 - x^2$}$$, what is the domain?

Accepted Answer

$$[-3, 3]$$

Question 7

Given the graph of $$y = f(x)$$ below (see $$image_3$$), which of the following best describes its symmetry?

Accepted Answer

The graph is symmetric about the $$y-$$axis.

Question 8

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

Accepted Answer

$$\frac{(x+h)^2$ - 3(x+h) - (x^2$ - 3x)}{h}$$

Question 9

Evaluate $$f(g(3))$$ using the graphs in $$image_4$$, where $$f(x)$$ and $$g(x)$$ are shown.

Accepted Answer

Find $$g(3)$$ from the graph, then use that value as input for $$f(x).$$

Question 10

Which of the following statements is true about even and odd functions?

Accepted Answer

An even function satisfies $$f(-x) = f(x)$$ and is symmetric about the $$y-$$axis.

Question 11

Which of the following real-world scenarios can be modeled by a function?

Accepted Answer

Assigning each person in a city their unique social security number.

Question 12

Given $$h(x) = \frac{3x^2$ - 1}{x-2}$$, what is the domain of $$h(x)$$?

Accepted Answer

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

Question 13

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

Accepted Answer

$$f(-x) = -f(x)$$ for all $$x in $$the domain.

Question 14

Suppose $$f(x) = x^3$ - x. Is$$ $$f(x)$$ even, odd, or neither?

Accepted Answer

Odd, because $$f(-x) = -f(x).$$

Question 15

Which of the following best describes the range of $$f(x) = x^2$ - 3x$$?

Accepted Answer

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

Question 16

Given $$f(x) = x^2$ - 3x$$, simplify the difference quotient $$\frac{f(x+h) - f(x)}{h}.$$

Accepted Answer

$$2x + h - 3$$

Question 17

Which of the following is NOT a property of a function?

Accepted Answer

Each output in the range is paired with exactly one input.

Question 18

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

Accepted Answer

$$9$$

Question 19

Which of the following best describes the symmetry of $$f(x) = x^4$ - 2x^2$ + 20$$?

Accepted Answer

Even, symmetric about the $$y-$$axis.

Review of Functions and Their Properties

Study Guide - Practice Questions