Question 1

Which of the following best describes the average rate of change of a function $$f(x)$$ from $$x = a to$$ $$x = b$$?

Accepted Answer

The slope of the secant line connecting $$(a, f(a))$$ and $$(b, f(b))$$

Question 2

Given the function $$f(x) = 6x^3$ - 12x + 5$$, use the formula for average rate of change to find the average rate of change from $$x = -2 to$$ $$x = 2.$$

Accepted Answer

$$
\frac{f(2) - f(-2)}{2 - (-2)} = \frac{21 - (-43)}{4} = 16$$

Question 3

A function $$f(x) is $$said to be increasing on an interval if:

Accepted Answer

For all $$a \u003c b in $$the interval, $$f(a) \u003c f(b)$$

Question 4

Which of the following intervals describes where the function $$f(x) is $$decreasing if $$f(x) is $$increasing on $$(-1, 1) \cup (3, \infty)$$?

Accepted Answer

$$(-\infty, -1) \cup (1, 3)$$

Question 5

What is the definition of a local maximum for a function $$f(x)$$?

Accepted Answer

A $$y-$$value greater than immediately surrounding $$y-$$values

Question 6

Given the points $$(1, 3)$$ and $$(3, 27) on $$the graph of a function, what is the average rate of change between these points?

Accepted Answer

$$12$$

Question 7

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

Accepted Answer

$$
m_{sec} = \frac{f(b) - f(a)}{b - a}$$

Question 8

Suppose $$g(x) = 3x^2$ - 2x + 3. $$What is the equation of the secant line containing $$(-2, g(-2))$$ and $$(1, g(1))$$?

Accepted Answer

$$y = 5x + 1$$

Question 9

Which of the following best describes a secant line to the graph of a function?

Accepted Answer

A line that passes through two points on the graph

Question 10

If a function $$f(x)$$ has an absolute maximum at $$x = 5$$, which of the following is true?

Accepted Answer

$$f(5) is $$the greatest $$y-$$value for the entire function

Question 11

Given $$f(x) = 5x^3$ + \frac{1}{4}x^2$ - 9$$, what is the degree of the polynomial?

Accepted Answer

$$3$$

Question 12

Which of the following is NOT a characteristic of a polynomial function?

Accepted Answer

The variable can appear in the denominator

Question 13

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

Accepted Answer

The rate of change is increasing

Question 14

Which of the following intervals describes where the function $$k(x) is $$concave down if it is concave up on $$(3, 6)$$ and concave down on $$(-\infty, 3)$$ and $$(6, 7)$$?

Accepted Answer

$$(-\infty, 3)$$ and $$(6, 7)$$

Question 15

Given the function $$f(x) = x + 2 - \sqrt{x}$$, which of the following is true?

Accepted Answer

It is not a polynomial function

Study Guide: Graphical Behavior, Maxima/Minima, Average Rate of Change, and Polynomial Functions

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