Question 1

Which of the following graphs represents a function? (Refer to the images provided: Graph 1, Graph 2, Graph 3.)

Accepted Answer

Only Graph 1

Question 2

What test can you use to determine if a graph represents a function?

Accepted Answer

Vertical-Line Test

Question 3

According to the vertical-line test, a graph is a function if and only if every vertical line intersects the graph in at most how many points?

Accepted Answer

One

Question 4

Given the point $$\left( \frac{\pi}{2}, 0 \right) on $$the graph in Graph 1, what does this tell you about the function $$f$$?

Accepted Answer

$$f\left( \frac{\pi}{2} \right) = 0$$

Question 5

If $$f(x) is $$the function represented by Graph 1, what is the $$y-$$intercept of the graph?

Accepted Answer

$$(0, 0)$$

Question 6

For the function in Graph 1, for which values of $$x$$ does $$f(x) = 2$$?

Accepted Answer

$$x = \frac{\pi}{4}, \frac{5\pi}{4}$$

Question 7

Which of the following best describes the domain of the function in Graph 1?

Accepted Answer

$$[0, 2\pi]$$

Question 8

Which of the following best describes the range of the function in Graph 1?

Accepted Answer

$$[-2, 2]$$

Question 9

Which of the following points is NOT on the graph of the function in Graph 1?

Accepted Answer

$$(\frac{\pi}{4}, -2)$$

Question 10

Suppose a vertical line $$x = a$$ intersects the graph in Graph 2 at two points. What does this indicate?

Accepted Answer

The graph does not represent a function.

Question 11

If $$f(x) is $$defined by the graph in Graph 1, for which values of $$x is$$ $$f(x) \u003c 0$$?

Accepted Answer

$$x \in \left( \frac{\pi}{2}, \pi \right) \cup \left( \frac{3\pi}{2}, 2\pi \right)$$

Question 12

Which of the following statements is true about the graph in Graph 3?

Accepted Answer

It fails the vertical-line test and is not a function.

Question 13

If $$f(x) is $$the function in Graph 1, what are the $$x-$$intercepts?

Accepted Answer

$$x = 0, \frac{\pi}{2}, \pi, \frac{3\pi}{2}, 2\pi$$

Question 14

If the point $$(a, b) is on $$the graph of a function $$f$$, which of the following is true?

Accepted Answer

$$f(a) = b$$

Precalculus Study Guide: Graphs of Functions and Their Properties

Study Guide - Practice Questions