Question 1

Which of the following best describes a function?

Accepted Answer

A correspondence between two sets where each element in the domain is paired with exactly one element in the range.

Question 2

Given the set of ordered pairs $$\{(1,2), (2,3), (3,4), (1,5)\}$$, is this a function?

Accepted Answer

No, because the input 1 is paired with two different outputs.

Question 3

Which of the following relations is a function?

Accepted Answer

$$\{(1,2), (2,3), (3,4), (4,5)\}$$

Question 4

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

Accepted Answer

$$f(-2) = 5$$

Question 5

Which of the following graphs passes the vertical line test and represents a function?

Accepted Answer

A parabola opening upwards

Question 6

Given $$f(x) = \sqrt{x-1}$$, what is the domain of $$f$$?

Accepted Answer

$$x \geq 1$$

Question 7

Which of the following is NOT a function?

Accepted Answer

$$x = y^2$

Question 8

If $$f(x) = \frac{1}{x-2}$$, which value is NOT in the domain of $$f$$?

Accepted Answer

$$x = 2$$

Question 9

Given the relation $$\{(1,2), (2,3), (3,4), (4,2)\}$$, what is the range?

Accepted Answer

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

Question 10

A real-world scenario: The temperature $$T (in $$degrees Celsius) at time $$t (in $$hours) is given by $$T(t) = 20 - 2t. $$What is the temperature after 5 hours?

Accepted Answer

$$T(5) = 12$$

Question 11

Which of the following best describes the vertical line test?

Accepted Answer

If any vertical line crosses the graph more than once, the graph is not a function.

Question 12

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

Accepted Answer

$$f(2) = -1$$

Question 13

Which of the following is the correct domain for $$f(x) = \frac{2x+1}{x^2$-9}$$?

Accepted Answer

$$x 
eq 3$$ and $$x 
eq -3$$

Question 14

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

Accepted Answer

$$f(g(2)) = 9$$

Question 15

Which of the following is a relation but NOT a function?

Accepted Answer

$$\{(1,2), (1,3), (2,4)\}$$

Functions and Graphs: Definitions, Examples, and Domain/Range

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