Question 1

Which of the following sets represents a function?

Accepted Answer

Set B: $$\{(1, 2), (3, 4), (6, 5), (8, 5)\}$$

Question 2

Given the equation $$x^2 + y = 4$, does this equation represent y$ as a function of x$?

Accepted Answer

Yes, because for every $$x$$ there is exactly one $$y$$ output.

Question 3

Which of the following best describes the domain of a relationship?

Accepted Answer

The set of all first components of the ordered pairs.

Question 4

A medical researcher records patient IDs and their blood pressure readings. Which is the explanatory variable?

Accepted Answer

Patient IDs

Question 5

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

Accepted Answer

$$f(-2) = 3$$

Question 6

Which of the following equations fails the vertical line test and is NOT a function?

Accepted Answer

$$x^2$$ + $$y^2 = 4$

Question 7

If $$f(x) = 0.012x^2$ - 0.2x + 8.7$$, what is $$f(30)$$?

Accepted Answer

$$f(30) = 13.5$$

Question 8

Which statement about functions is correct?

Accepted Answer

A function assigns exactly one output to each input.

Question 9

Given the set $$\{(0, 9.1), (10, 6.7), (20, 10.7), (30, 13.2), (42, 21.7)\}$$, what is the range?

Accepted Answer

$$\{9.1, 6.7, 10.7, 13.2, 21.7\}$$

Question 10

Which of the following is the correct interval notation for the domain $$x$$ such that $$-4 \leq x \leq 6$$?

Accepted Answer

$$[-4, 6]$$

Question 11

A chemical reaction is modeled by $$f(x) = 2x + 4. If $$the input $$x$$ represents the amount of reactant, what is the output when $$x = 2$$?

Accepted Answer

$$f(2) = 8$$

Question 12

Which of the following is NOT a function?

Accepted Answer

A set where one input has two different outputs.

Question 13

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

Accepted Answer

Question 14

Which of the following is the correct set builder notation for the domain $$x$$ such that $$-2 \u003c x \leq 4$$?

Accepted Answer

$$\{x | -2 \u003c x \leq 4\}$$

Question 15

A graph passes the vertical line test. What does this indicate?

Accepted Answer

The graph represents a function.

Question 16

If $$f(x) = 2x$$, what is the output for $$x = -1$$?

Accepted Answer

$$f(-1) = -2$$

Question 17

Which of the following statements about domain and range is correct?

Accepted Answer

Range is the set of all possible outputs.

Question 18

Given $$x^2$$ + $$y^2 = 4$, what is the output for x = 1$?

Accepted Answer

$$y = \pm 3$$

Question 19

Which of the following is the correct interval notation for the range $$y$$ such that $$1 \leq y \leq 3$$?

Accepted Answer

$$[1, 3]$$

Question 20

A real-world scenario: A company tracks employee names and their sales numbers. Which is the response variable?

Accepted Answer

Sales numbers

Functions and Relations: Definitions, Properties, and Notation

Study Guide - Practice Questions