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 x-value 2 is paired with two different y-values.

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 $$g is $$defined by $$g(x) = x^2$ - 5x + 6. $$What is the value of $$g(-1)$$?

Accepted Answer

$$12$$

Question 6

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

Accepted Answer

If every vertical line intersects a graph at most once, the graph defines y as a function of x.

Question 7

Given the graph of a function, how do you find the x-intercepts?

Accepted Answer

Look for the points where the graph crosses the x-axis.

Question 8

Which of the following is the correct definition of a function?

Accepted Answer

A correspondence from the domain to the range such that each element in the domain corresponds to exactly one element in the range.

Question 9

If the graph of $$g(x) is $$the graph of $$f(x)$$ shifted down 3 units, which equation represents $$g(x)$$?

Accepted Answer

$$g(x) = f(x) - 3$$

Question 10

Suppose the domain of a function $$h is$$ $$\{1, 2, 3, 4\}$$ and the range is $$\{5, 6, 7\}. $$Which of the following could be a possible set of ordered pairs for $$h$$?

Accepted Answer

$$\{(1, 5), (2, 6), (3, 7), (4, 5)\}$$

Question 11

A function $$f is $$graphed and passes through the points $$(-2, 0)$$, $$(0, 4)$$, and $$(3, -1). $$What is the y-intercept of $$f$$?

Accepted Answer

$$4$$

Question 12

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 13

If $$f(x) = x^2$ and g(x) = f(x) - 4$, what is the range of g(x$$)$$?

Accepted Answer

$$[-4, \infty)$$

Question 14

Which of the following is NOT a valid way to evaluate a function $$f at$$ $$x = 3$$?

Accepted Answer

$$f(x) = 3$$

Question 15

A function $$f is $$defined by $$f(x) = \sqrt{x-2}. $$What is the domain of $$f$$?

Accepted Answer

$$[2, \infty)$$

Question 16

If a function's graph passes the vertical line test, which of the following must be true?

Accepted Answer

Each x-value corresponds to exactly one y-value.

Question 17

Given the function $$f(x) = 2x + 1$$, which of the following points is on the graph of $$f$$?

Accepted Answer

$$(1, 3)$$

Question 18

Which of the following best describes the range of a function from its graph?

Accepted Answer

All the y-values for which the graph exists.

Question 19

A function $$f is $$defined by $$f(x) = \frac{1}{x-2}. $$What is the domain of $$f$$?

Accepted Answer

$$(-\infty, 2) \cup (2, \infty)$$

Functions and Their Graphs: Foundations for Precalculus

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