Question 1

Which of the following sets of ordered pairs represents a function?

Accepted Answer

$$\{(2, 5), (3, 6), (4, 7)\}$$

Question 2

Given the relation $$\{(2, 4), (3, 5), (4, 6), (2, 7)\}$$, is this relation a function?

Accepted Answer

No, because the x-value 2 is paired with two different y-values.

Question 3

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

Accepted Answer

The set of all possible x-values.

Question 4

A relation is defined by the equation $$y = \sqrt{x-3}. $$What is the domain of this relation?

Accepted Answer

$$x \geq 3$$

Question 5

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

Accepted Answer

$$y = \pm \sqrt{x}$$

Question 6

A relation is given by the table: $$\{(1, 2), (2, 3), (3, 4), (4, 5)\}. $$What is the range?

Accepted Answer

$$\{2, 3, 4, 5\}$$

Question 7

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

Accepted Answer

If every vertical line crosses the graph at most once, the graph is a function.

Question 8

Suppose a relation is defined by $$y = \frac{1}{x-2}. $$What value must be excluded from the domain?

Accepted Answer

$$x = 2$$

Question 9

A real-world scenario: The temperature $$T (in $$degrees Celsius) at time $$t (in $$hours) is given by $$T = 20 - 2t. Is $$this a function?

Accepted Answer

Yes, because each time $$t$$ corresponds to exactly one temperature $$T.$$

Question 10

Given the relation $$y = \sqrt{9 - x^2$}$$, what is the domain?

Accepted Answer

$$-3 \leq x \leq 3$$

Question 11

Which of the following is NOT a valid way to define a relation?

Accepted Answer

As a single number

Question 12

If a relation is defined by $$y = \frac{2}{x}$$, what is the range if the domain is all real numbers except $$x = 0$$?

Accepted Answer

All real numbers except $$y = 0$$

Question 13

A relation is given by the mapping: $$1 \rightarrow 2$$, $$2 \rightarrow 3$$, $$3 \rightarrow 2. Is $$this a function?

Accepted Answer

Yes, because each input has exactly one output.

Question 14

Which of the following best describes the range of a function?

Accepted Answer

The set of all possible y-values.

Question 15

A chemical reaction is modeled by $$C = 5t + 10$$, where $$C is $$the concentration (in mg/L) and $$t is $$time (in hours). What is the domain of this function in a real-world context?

Accepted Answer

All real numbers $$t \geq 0$$

Question 16

Which of the following relations is NOT a function?

Accepted Answer

$$x = y^2$

Question 17

If a relation is defined by $$y = \frac{1}{x-1}$$, which value must be excluded from the domain?

Accepted Answer

$$x = 1$$

Question 18

A relation is defined by $$y = \sqrt{x+4}. $$What is the domain?

Accepted Answer

$$x \geq -4$$

Question 19

Which of the following best describes a function?

Accepted Answer

A relation where each x-value is paired with exactly one y-value.

Question 20

A medical dosage is modeled by $$D = 50 - 2t$$, where $$D is $$the dosage in mg and $$t is $$time in hours. Is this a function?

Accepted Answer

Yes, because each time $$t$$ corresponds to exactly one dosage $$D.$$

Relations and Functions: Definitions, Domain, Range, and the Vertical Line Test

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