Question 1

Which of the following best describes the difference between a relation and a function?

Accepted Answer

A function pairs each element of the domain with exactly one element of the range, while a relation can pair an element of the domain with multiple elements of the range.

Question 2

Given the set of ordered pairs $$\{(1, 6), (3, 9), (6, 1), (9, 2)\}$$, what is the domain?

Accepted Answer

$$\{1, 3, 6, 9\}$$

Question 3

Which of the following is NOT a way to represent a relation?

Accepted Answer

Using a histogram

Question 4

Suppose a scientist records the average high temperature in Los Angeles for the first five months of the year as shown in the table below. What is the range of this relation?

Month: January, February, March, April, May
Temperature: 68°F, 69°F, 70°F, 73°F, 74°F

Accepted Answer

$$\{68, 69, 70, 73, 74\}$$

Question 5

Which of the following equations does NOT define $$y as a $$function of $$x$$?

Accepted Answer

$$x = y^2$

Question 6

If $$f(x) = 2x - 5$$, what is $$f(3)$$?

Accepted Answer

$$-1$$

Question 7

A function is given by $$f(x) = \frac{1}{x-2}. $$What is the domain of $$f$$?

Accepted Answer

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

Question 8

Given the function $$f(x) = \sqrt{x-3}$$, which of the following values is NOT in the domain?

Accepted Answer

$$x = 2$$

Question 9

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

Accepted Answer

$$7$$

Question 10

Which of the following best describes the difference quotient for a function $$f$$?

Accepted Answer

$$\frac{f(x+h) - f(x)}{h}$$

Question 11

A right triangle has one leg of length $$x$$ and the other leg is triple the length of the shorter leg. Express the area $$A as a $$function of $$x$$ and state the domain for a real-world application.

Accepted Answer

$$A(x) = \frac{1}{2}x(3x)$$,\; x \u003e 0$

Question 12

If $$f(x) = x^2$ and g(x) = x - 1$, what is the domain of $$\frac{f}{g}$$?

Accepted Answer

$$(-\infty, 1) \cup (1, \infty)$$

Question 13

Which of the following real-world scenarios is best modeled by a function?

Accepted Answer

Assigning each person in a class to their student ID number

Question 14

Given $$f(x) = x^2$ + 2x$$ and $$g(x) = 3x - 1$$, find $$(f-g)(1).$$

Accepted Answer

$$0$$

Question 15

Which of the following is a correct interpretation of the mapping diagram shown in the fourth image?

Accepted Answer

Each element in the domain is paired with exactly one element in the range.

Question 16

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

Accepted Answer

$$[0, \infty)$$

Question 17

Which of the following statements about the function machine (second image) is correct?

Accepted Answer

For each input $$x$$, there is exactly one output $$y = f(x).$$

Question 18

Given $$f(x) = x^2$ and g(x) = 2x$, what is (fg)(3$$)$$?

Accepted Answer

$$36$$

Question 19

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

Accepted Answer

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

Functions and Their Graphs: Fundamental Concepts and Representations

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