Question 1

Given the function $$f(x) = x^2$ - 2x + 3$$, what is the average rate of change of $$f(x)$$ from $$x = 1 to$$ $$x = 4$$?

Accepted Answer

$$3$$

Question 2

Which of the following best describes the average rate of change (AROC) of a function $$f(x)$$ between $$x = a$$ and $$x = b$$?

Accepted Answer

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

Question 3

A toy rocket is launched and its height after $$t$$ seconds is given by $$h(t) = -16t^2$ + 128t. $$What is the average rate of change of height between $$t = 3$$ and $$t = 4$$ seconds?

Accepted Answer

$$-80 ft/sec$$

Question 4

Given the table below for $$F(x)$$:

$$x$$: $$10$$, $$13$$, $$18$$, $$21$$
$$F(x)$$: $$32$$, $$48$$, $$64$$, $$75$$

What is the average rate of change of $$F(x)$$ from $$x = 13 to$$ $$x = 18$$?

Accepted Answer

$$3.2$$

Question 5

If the average rate of change of a function $$f(x)$$ between $$x = 2$$ and $$x = 5 is $$negative, what does this indicate about the function on that interval?

Accepted Answer

The function is decreasing between $$x = 2$$ and $$x = 5$$

Question 6

Given $$f(x) = x^2$ + 2x + 1$$, what is the simplified formula for the average rate of change between $$x = a$$ and $$x = a + h$$?

Accepted Answer

$$2a + h + 2$$

Question 7

A temperature sensor records $$T(8) = 45^	ext{o}F at 8$$:00 am and $$T(16) = 65^	ext{o}F at 4$$:00 pm. What is the average rate of change of temperature per hour between these times?

Accepted Answer

$$2.5^	ext{o}F/hr$$

Question 8

Given the function $$g(x) = 2x + 5$$, what is the average rate of change between $$x = 1$$ and $$x = 4$$?

Accepted Answer

$$2$$

Question 9

If the graph of a function is a straight line, what can you say about its average rate of change between any two points?

Accepted Answer

It is constant and equal to the slope of the line

Question 10

Given $$f(x) = x^2$, what is the average rate of change from x = 2$ to x = 5$?

Accepted Answer

$$7$$

Question 11

A function $$f(x) is $$decreasing throughout an interval, but the average rate of change between two points is zero. What does this imply?

Accepted Answer

The function is constant between those points

Question 12

Given $$f(x) = x^2$ - 4x + 7$$, what is the average rate of change from $$x = 0 to$$ $$x = 3$$?

Accepted Answer

$$-2$$

Question 13

If the average rate of change of a function $$f(x)$$ between $$x = a$$ and $$x = b is $$positive, which of the following must be true?

Accepted Answer

$$f(b) \u003e f(a)$$

Question 14

Given $$f(x) = 3x^2$ + 2x$$, what is the average rate of change from $$x = 1 to$$ $$x = 4$$?

Accepted Answer

$$18$$

Question 15

A function $$f(x) is $$graphed and the secant line between $$x = 2$$ and $$x = 6$$ has a slope of $$-3. $$What is the average rate of change of $$f(x)$$ over this interval?

Accepted Answer

$$-3$$

Question 16

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

Accepted Answer

$$5$$

Question 17

If the average rate of change of a function $$f(x)$$ between $$x = 1$$ and $$x = 5 is$$ $$0$$, what does this tell you about $$f(x) on $$this interval?

Accepted Answer

The function is constant between $$x = 1$$ and $$x = 5$$

Question 18

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

Accepted Answer

$$2a + h$$

Question 19

A car travels such that its position at time $$t is $$given by $$s(t) = 4t^2$ + 2t. $$What is the average rate of change of position from $$t = 1 to$$ $$t = 3$$?

Accepted Answer

$$26$$

Question 20

If the average rate of change of a function $$f(x)$$ between $$x = 2$$ and $$x = 6 is$$ $$0$$, which of the following is true?

Accepted Answer

$$f(2) = f(6)$$

B4

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