Question 1

Which of the following statements correctly describes an even function?

Accepted Answer

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

Question 2

Given the function $$h(x) = x^3$ + 4x$$, determine whether $$h(x) is $$even, odd, or neither.

Accepted Answer

Odd, because $$h(-x) = -h(x)$$

Question 3

Which of the following graphs represents an odd function?

Accepted Answer

A graph symmetric with respect to the origin

Question 4

Let $$f(x) = 2x^2$ + 3. Is$$ $$f(x)$$ even, odd, or neither?

Accepted Answer

Even, because $$f(-x) = f(x)$$

Question 5

For the function $$F(x) = 1 + |x|$$, which of the following is true?

Accepted Answer

$$F(x) is $$even

Question 6

A function $$f is $$increasing on an interval $$I if$$:

Accepted Answer

For any $$x_1$$ \u003c $$x_2 in$$ $$I$$, $$f(x_1$) \u003c f(x_2$)$$

Question 7

Suppose the graph of a function $$f$$ has a local maximum at $$x = 2$$ and a local minimum at $$x = 5. $$Which statement is true?

Accepted Answer

$$f(2) is $$greater than $$f(x)$$ for all $$x$$ near $$2$$, and $$f(5) is $$less than $$f(x)$$ for all $$x$$ near $$5$$

Question 8

Which of the following is the definition of the average rate of change of a function $$f$$ from $$a to$$ $$b$$?

Accepted Answer

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

Question 9

If $$g(x) = x^2$ - 3x + 2$$, what is the average rate of change of $$g$$ from $$x = 1 to$$ $$x = 3$$?

Accepted Answer

$$1$$

Question 10

Given $$f(x) = x^2$ + 1$$, what is the average rate of change from $$x = 0 to$$ $$x = 2$$?

Accepted Answer

$$2$$

Question 11

Which theorem guarantees that a continuous function on a closed interval $$[a, b]$$ has both an absolute maximum and an absolute minimum?

Accepted Answer

Extreme Value Theorem

Question 12

Suppose $$f(x) is $$constant on the interval $$[2, 5]. $$Which of the following is true about the average rate of change of $$f on$$ $$[2, 5]$$?

Accepted Answer

It is equal to $$0$$

Question 13

A function $$f$$ has a domain $$[0, 5]$$ and attains its largest value at $$x = 3$$ and its smallest value at $$x = 5. $$What are the absolute maximum and minimum values?

Accepted Answer

Absolute maximum: $$f(3)$$, Absolute minimum: $$f(5)$$

Question 14

If the graph of $$f is $$symmetric with respect to the $$y-$$axis, which of the following must be true?

Accepted Answer

$$f(x) is $$even

Question 15

Which of the following intervals describes where a function is decreasing if for all $$x_1  f$$($$x_2$$)$$?

Accepted Answer

The function is decreasing on the interval

Question 16

A secant line to the graph of $$f$$ passes through $$(a, f(a))$$ and $$(b, f(b)). $$What is the slope of this secant line?

Accepted Answer

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

Question 17

Suppose $$g(x) = x^2$ - 3x + 2. $$Find the equation of the secant line passing through $$(1, g(1))$$ and $$(3, g(3)).$$

Accepted Answer

$$y = x - 1$$

Question 18

Which of the following is a real-world example of a function with a local maximum but no absolute maximum?

Accepted Answer

The height of a ball thrown upward, measured over all time

Properties of Functions: Even and Odd Functions, Graph Symmetry, and Algebraic Identification

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