Question 1

Which of the following statements correctly describes an even function?

Accepted Answer

A function $$f is $$even if, for every $$x in $$its domain, $$f(-x) = f(x).$$

Question 2

Given the graph of $$f(x)$$ shown in the second image, on which interval is the function increasing?

Accepted Answer

$$(0, 3)$$

Question 3

Which of the following is true for an odd function $$f$$?

Accepted Answer

For every $$x in $$the domain, $$f(-x) = -f(x).$$

Question 4

Refer to the fourth image. What are the local maximum values of the function?

Accepted Answer

$$3 at$$ $$x = 0$$

Question 5

A function $$f is $$said to be decreasing on an interval $$I if$$:

Accepted Answer

For any $$x_1  f$$($$x_2$$)$$.

Question 6

Which of the following best describes the symmetry of the function shown in the first image?

Accepted Answer

Symmetric with respect to the y-axis

Question 7

Given the function $$f(x) = x^3$ - x$$, determine if it is even, odd, or neither.

Accepted Answer

Odd

Question 8

Refer to the sixth image. At which $$x-$$value does the function have a local minimum?

Accepted Answer

$$x = 3$$

Question 9

Which of the following is the correct formula for the average rate of change of a function $$f$$ from $$x = a to$$ $$x = b$$?

Accepted Answer

$$\frac{f(b) - f(a)}{b - a}$$

Question 10

According to the Extreme Value Theorem, if a function $$f is $$continuous on a closed interval $$[a, b]$$, then:

Accepted Answer

$$f$$ has both an absolute maximum and an absolute minimum on $$[a, b].$$

Question 11

If a function $$f is $$constant on an interval $$I$$, what can be said about its graph on $$I$$?

Accepted Answer

The graph is a horizontal line segment on $$I.$$

Question 12

Given the function $$f(x) = x^2$ + 1$$, determine if it is even, odd, or neither.

Accepted Answer

Even

Question 13

Suppose $$f(x)$$ has a local maximum at $$x = c. $$Which of the following must be true?

Accepted Answer

$$f(c) \geq f(x)$$ for all $$x in $$some open interval containing $$c.$$

Question 14

Refer to the seventh image. What is the absolute minimum value of the function on $$[a, b]$$?

Accepted Answer

$$f(v)$$

Question 15

If the average rate of change of $$f(x)$$ from $$x = 2 to$$ $$x = 5 is$$ $$4$$, and $$f(2) = 3$$, what is $$f(5)$$?

Accepted Answer

$$f(5) = 15$$

Question 16

Which of the following real-world scenarios best represents a function that is increasing on an interval?

Accepted Answer

The temperature rises steadily from 8 AM to 12 PM.

Question 17

Given the function $$f(x) = x^4$ - 2x^2$, is it even, odd, or neither?

Accepted Answer

Even

Question 18

If a function $$f is $$increasing on $$(-\infty, 2)$$ and decreasing on $$(2, \infty)$$, what can be said about $$x = 2$$?

Accepted Answer

$$f$$ has a local maximum at $$x = 2$$

Question 19

Which of the following is NOT a property of an even function?

Accepted Answer

The graph is symmetric with respect to the origin.

Question 20

Suppose the secant line passes through the points $$(2, 5)$$ and $$(6, 13) on $$the graph of $$f(x). $$What is the slope of the secant line?

Accepted Answer

$$2$$

Properties of Functions: Even/Odd Functions, Intervals, and Extrema

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