Question 1

Which of the graphs shown above represents the graph of a function?

Accepted Answer

Only the first graph

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

One point

Question 3

Given the point $$\left(\frac{\pi}{2}, 0\right) on $$the first graph, what is the value of $$f\left(\frac{\pi}{2}\right)$$?

Accepted Answer

$$0$$

Question 4

Which of the following statements is true about the second graph?

Accepted Answer

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

Question 5

For the first graph, what is the range of the function $$f$$?

Accepted Answer

$$[-2, 2]$$

Question 6

What are the $$x-$$intercepts of the function shown in the first graph?

Accepted Answer

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

Question 7

If $$f(x) is $$the function represented by the first graph, for which values of $$x$$ does $$f(x) = 2$$?

Accepted Answer

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

Question 8

Which of the following best describes the domain of the function in the first graph?

Accepted Answer

$$[0, 2\pi]$$

Question 9

Suppose the second graph is given by the equation $$x = y^2$. Which of the following is true?

Accepted Answer

It is not a function because some $$x-$$values correspond to two $$y-$$values.

Question 10

For the first graph, what is the $$y-$$intercept?

Accepted Answer

$$(0, 0)$$

Question 11

If the third graph is given by $$y^2$$ - $$x^2 = 1$, which of the following statements is correct?

Accepted Answer

It is not a function because some $$x-$$values correspond to two $$y-$$values.

Question 12

Which of the following real-world scenarios best illustrates the vertical-line test for a function?

Accepted Answer

A vending machine that gives exactly one snack for each button pressed.

Question 13

If $$f(x) is $$the function in the first graph, for which values of $$x$$ does $$f(x) = -2$$?

Accepted Answer

$$x = \frac{3\pi}{4}, \frac{7\pi}{4}$$

Question 14

Which of the following is NOT a property of the function shown in the first graph?

Accepted Answer

It is defined for all real numbers.

Question 15

If the function in the first graph models the height (in meters) of a point on a Ferris wheel as it rotates, what does the range $$[-2, 2]$$ represent?

Accepted Answer

The minimum and maximum heights reached by the point.

Graphs of Functions: Identification and Analysis

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