Question 1

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

Accepted Answer

Only Image 1

Question 2

According to the Vertical-Line Test, a set of points in the $$xy-$$plane is the graph of a function if and only if every vertical line intersects the graph in at most how many points?

Accepted Answer

$$1$$

Question 3

Given the point $$\left( \frac{\pi}{2}, 0 \right) on $$the graph in Image 1, what is $$f\left( \frac{\pi}{2} \right)$$?

Accepted Answer

$$0$$

Question 4

If $$f(x) is $$the function graphed in Image 1, what is the range of $$f$$?

Accepted Answer

$$[-2, 2]$$

Question 5

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

Accepted Answer

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

Question 6

For the graph in Image 2, does the graph represent a function? Why or why not?

Accepted Answer

No, because some vertical lines intersect the graph at more than one point.

Question 7

Suppose $$f is a $$function and $$(a, b) is a $$point on its graph. Which of the following statements is true?

Accepted Answer

$$f(a) = b$$

Question 8

If the graph of a function $$f$$ contains the point $$(2, -3)$$, which of the following is true?

Accepted Answer

$$f(2) = -3$$

Question 9

Which of the following best describes the domain of the function graphed in Image 1?

Accepted Answer

$$[0, 2\pi]$$

Question 10

For the graph in Image 3, which of the following statements is true?

Accepted Answer

It is not the graph of a function because some vertical lines intersect the graph at two points.

Question 11

If $$f(x) is $$the function graphed in Image 1, for which value of $$x$$ does $$f(x)$$ attain its minimum value?

Accepted Answer

$$x = \frac{3\pi}{4}$$

Question 12

Which of the following is a $$y-$$intercept of the function graphed in Image 1?

Accepted Answer

$$(0, 0)$$

Question 13

If a vertical line intersects a graph at three points, what can you conclude?

Accepted Answer

The graph is not the graph of a function.

Functions and Their Graphs: Identifying and Analyzing Graphs of Functions

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