Question 1

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

Accepted Answer

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

Question 2

Given the function $$f(x) = 2x^2$ - x + 3$$, what is $$f(-7)$$?

Accepted Answer

$$108$$

Question 3

Which of the following relations is NOT a function?

Accepted Answer

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

Question 4

If $$f(x) = \sqrt{x+4}$$, what is the domain of $$f$$?

Accepted Answer

$$x \geq -4$$

Question 5

A graph passes the vertical-line test if:

Accepted Answer

No vertical line intersects the graph more than once.

Question 6

Given $$h(x) = \dfrac{3x+7}{x^2$+2x-3}$$, which values are NOT in the domain?

Accepted Answer

$$x = -3$$ and $$x = 1$$

Question 7

If $$f(x) = x^2$ - 6$$, what is the range of $$f$$?

Accepted Answer

$$[-6, \infty)$$

Question 8

Which statement best describes the difference between a relation and a function?

Accepted Answer

A function assigns exactly one output to each input, while a relation may assign multiple outputs to an input.

Question 9

Given $$f(x) = \dfrac{1}{x-3}$$, which of the following statements is true?

Accepted Answer

$f(3)$$ does not exist because it results in division by zero.

Question 10

A hospital records the temperature of a patient every hour. Which of the following best describes the relationship between time and temperature?

Accepted Answer

It is a function because each hour has exactly one recorded temperature.

Question 11

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

Accepted Answer

$$6$$

Question 12

Which of the following is the correct notation for the value of a function $$f at$$ $$x$$?

Accepted Answer

$$f(x)$$

Question 13

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

Accepted Answer

$$\{1, 2\}$$

Question 14

A function $$f is $$defined by $$f(x) = 2x^2$ - x + 3. $$What is $$f(a-4)$$?

Accepted Answer

$$2a^2 - 17a + 39$

Question 15

Which of the following graphs could NOT represent a function?

Accepted Answer

A graph where a vertical line crosses the graph at two points.

Question 16

If $$f(x) = \sqrt{x+4}$$, what is the range of $$f$$?

Accepted Answer

$$[0, \infty)$$

Question 17

Which of the following is a real-world example of a function?

Accepted Answer

Assigning each student in a class their unique student ID number.

Question 18

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

Accepted Answer

$$4$$

Question 19

If $$f(x) = \dfrac{1}{x-3}$$, which of the following is in the domain of $$f$$?

Accepted Answer

$$x = -3$$

Functions and Graphs: Fundamental Concepts and Applications

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