Question 1

Which of the following best describes the domain of the relation $$\{(0, 9.1), (10, 6.7), (20, 10.7), (30, 13.2), (40, 21.2)\}$$?

Accepted Answer

$$\{0, 10, 20, 30, 40\}$$

Question 2

Given the relation $$\{(1, 2), (3, 4), (6, 5), (8, 5)\}$$, is this relation a function?

Accepted Answer

Yes, because each x-value corresponds to exactly one y-value.

Question 3

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

Accepted Answer

$$x = y^2$

Question 4

If $$f(x) = 2x^2$ - 7x + 2$$, what is $$f(-5)$$?

Accepted Answer

$$2(-5)^2 - 7(-5) + 2 = 50 + 35 + 2 = 87$

Question 5

Which of the following graphs passes the vertical line test and therefore represents $$y as a $$function of $$x$$?

Accepted Answer

A graph where a vertical line crosses the curve at only one point everywhere.

Question 6

Refer to the T Cell Count and HIV Infection graph. What is the domain of the function $$y = f(x)$$ shown?

Accepted Answer

$$0 \leq x \leq 11$$

Question 7

Refer to the T Cell Count and HIV Infection graph. What is the range of the function $$y = f(x)$$?

Accepted Answer

$$200 \leq y \leq 1200$$

Question 8

Given the graph of $$y = f(x) in $$the third image, what is the domain of the function?

Accepted Answer

$$-2 \leq x \leq 2$$

Question 9

Given the graph of $$y = f(x) in $$the third image, what is the range of the function?

Accepted Answer

$$-2 \leq y \leq 4$$

Question 10

Given the graph of $$y = f(x) in $$the fourth image, what are the x- and y-intercepts?

Accepted Answer

x-intercept: $$x = 1$$, y-intercept: $$y = -2$$

Question 11

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

Accepted Answer

The set of all y-values for which the graph exists.

Question 12

A function $$f(x) is $$defined as $$f(x) = 2x - 3. $$What is the y-intercept of its graph?

Accepted Answer

$$y = -3$$

Question 13

A function can have:

Accepted Answer

More than one x-intercept but at most one y-intercept.

Question 14

If $$f(x) = 2x$$, which of the following points lies on the graph of $$f(x)$$?

Accepted Answer

$$(2, 4)$$

Question 15

Suppose a function $$f$$ models the cost $$C (in $$dollars) to produce $$x$$ units of a product as $$C = f(x) = 5x + 100. $$What does $$f(20)$$ represent in this context?

Accepted Answer

The cost to produce 20 units.

Basics of Functions and Their Graphs

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