Question 1

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

Accepted Answer

The set of all first components of the ordered pairs.

Question 2

Given the relation $$\{(2, 5), (3, 7), (2, 8)\}$$, is this relation a function?

Accepted Answer

No, because the element 2 in the domain corresponds to two different elements in the range.

Question 3

Which equation does NOT define $$y as a $$function of $$x$$?

Accepted Answer

$$x = y^2$

Question 4

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

Accepted Answer

$$2$$

Question 5

A function $$g(x) is $$graphed and a vertical line crosses the graph at two points. What does this indicate?

Accepted Answer

The graph does not represent a function.

Question 6

Which of the following is the correct function notation for 'f at x'?

Accepted Answer

$$f(x)$$

Question 7

Given the graph of a function, how do you determine the range?

Accepted Answer

Look for all the outputs on the y-axis that correspond to points on the graph.

Question 8

Suppose $$h(x) = x^2$ - 4x + 3. $$What is the y-intercept of the graph of $$h$$?

Accepted Answer

$$3$$

Question 9

A function $$f is $$graphed and crosses the x-axis at $$x = -2$$ and $$x = 3. $$What are the x-intercepts?

Accepted Answer

$$(-2, 0)$$ and $$(3, 0)$$

Question 10

Which of the following real-world scenarios can be modeled by a function?

Accepted Answer

Assigning each person in a city to their birth date.

Question 11

If $$f(x) = x^2$ and g(x$$) = $$x^2 - 3$, how is the graph of g$ related to the graph of f$?

Accepted Answer

The graph of $$g is $$shifted down 3 units from $$f.$$

Question 12

Which of the following sets is the range of the relation $$\{(1, 2), (2, 4), (3, 2), (4, 5)\}$$?

Accepted Answer

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

Question 13

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

Accepted Answer

$$x \geq 1$$

Question 14

If a graph passes the vertical line test, what does this mean?

Accepted Answer

Every $$x$$ value has exactly one $$y$$ value.

Question 15

Given the function $$f(x) = 2x + 1$$, what is $$f(-3)$$?

Accepted Answer

$$-5$$

Question 16

Which of the following statements is TRUE about the y-intercept of a function's graph?

Accepted Answer

A function can have at most one y-intercept.

Question 17

Suppose a function $$f is $$graphed and the domain is $$[-2, 5]. $$Which of the following could be the range?

Accepted Answer

$$[0, 10]$$

Question 18

If $$f(x) = x^2$ and f(a) = 16$, what is a possible value of a$?

Accepted Answer

$$4$$

Question 19

Which of the following is NOT a function?

Accepted Answer

Assigning each person to all their phone numbers.

Question 20

If $$f(x) = x + 2$$ and $$g(x) = 2x$$, what is $$f(g(3))$$?

Accepted Answer

$$8$$

Functions and Their Graphs: Foundations for Precalculus

Study Guide - Practice Questions