Question 1

Which of the following best describes the domain of a function $$f$$?

Accepted Answer

The set of all possible input values of $$f$$

Question 2

Given the graph of a function $$f(x)$$, which interval shows $$f(x) is $$increasing?

Accepted Answer

$$f(x) is $$increasing where the graph moves upward from left to right.

Question 3

If a function $$f is $$concave down on an interval, what does this mean about its rate of change?

Accepted Answer

The rate of change is decreasing.

Question 4

Which of the following statements is true about the independent and dependent variables in a function?

Accepted Answer

The independent variable is the input and the dependent variable is the output.

Question 5

A water tank is being drained. The diameter of the water surface is decreasing, but at an increasing rate. Which of the following best describes the behavior of the function modeling the diameter?

Accepted Answer

The function is decreasing and concave up.

Question 6

If $$f(x) is $$concave up on the interval $$[a, b]$$, which of the following is true?

Accepted Answer

The rate of change of $$f(x) is $$increasing.

Question 7

Given the graph of $$f(x)$$, how can you determine where $$f(x) is $$decreasing?

Accepted Answer

Where the graph moves downward from left to right.

Question 8

Suppose $$f(x) is $$increasing on the interval $$[2, 5]$$ and decreasing on $$[5, 8]. $$What can you say about $$x = 5$$?

Accepted Answer

$$x = 5 is a $$local maximum.

Question 9

Which of the following best describes a function?

Accepted Answer

A relation where each input has exactly one output.

Question 10

If the graph of $$f(x) is $$concave down on $$[a, b]$$, what does this imply about the second derivative $$f''(x) on $$that interval?

Accepted Answer

$$f''(x) \u003c 0$$

Question 11

A function $$h$$ models the height of a ball thrown upward. At the peak of its path, which of the following is true?

Accepted Answer

The rate of change of $$h is $$zero.

Question 12

Which of the following is NOT a valid way to represent a function?

Accepted Answer

Histogram

Question 13

If $$f(x) is $$decreasing and concave up on an interval, which of the following is true?

Accepted Answer

The rate of change is negative and increasing.

Question 14

Which of the following best describes the behavior of $$f(x) if it is $$increasing and concave down on $$[a, b]$$?

Accepted Answer

The rate of change is positive and decreasing.

Question 15

If a function $$f is $$defined by the table below, which value is the output when the input is $$x = 3$$?

$$x$$: $$1, 2, 3, 4$$

$$f(x)$$: $$5, 7, 9, 11$$

Accepted Answer

$$f(3) = 9$$

Question 16

Which of the following intervals shows where the graph of $$f(x) is $$decreasing?

Accepted Answer

$$x$$ values where the graph moves downward from left to right.

Question 17

If the rate of change of $$h is $$decreasing, which of the following is true about the graph of $$h$$?

Accepted Answer

The graph is concave down.

Question 18

A function $$f is $$defined for $$x in$$ $$[0, 10]. If$$ $$f(x) is $$increasing on $$[0, 3]$$ and $$[7, 10]$$, which intervals is $$f(x)$$ increasing?

Accepted Answer

$$[0, 3]$$ and $$[7, 10]$$

Change in Tandem: Graphical Behavior and Rate of Change in Functions

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