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

$$5.33$$

Question 2

The average rate of change (AROC) between two points $$(x_1$, f(x_1$))$$ and $$(x_2$, f(x_2$)) on a $$function is equivalent to:

Accepted Answer

The slope of the secant line between $$x_1$$ and $$x_2$$

Question 3

Suppose the height of a rocket is given by $$h(t) = -16t^2$ + 120t. $$What is the average rate of change of height from $$t = 2 to$$ $$t = 4$$ seconds?

Accepted Answer

$$-40 ft/sec$$

Question 4

Given the table of values for $$F(x)$$:

$$x$$: $$10$$, $$12$$, $$15$$, $$18$$, $$21$$

$$F(x)$$: $$32$$, $$48$$, $$64$$, $$83$$, $$99$$

What is the average rate of change of $$F(x)$$ from $$x = 12 to$$ $$x = 18$$?

Accepted Answer

$$5.83$$

Question 5

If the average rate of change of a function between two points is negative, what does this tell you about the function on that interval?

Accepted Answer

The function is decreasing on that interval.

Question 6

Given $$f(x) = x^2$ + 2x + 1$$, find the average rate of change from $$x = -1 to$$ $$x = 2.$$

Accepted Answer

$$5$$

Question 7

A temperature function $$T(t)$$ models the temperature throughout a day. If $$T(8) = 60^\circ F$$ and $$T(16) = 76^\circ F$$, what is the average rate of change of temperature between 8 am and 4 pm?

Accepted Answer

$$2^\circ F/hr$$

Question 8

Given $$f(x) = 2x + 5$$, what is the average rate of change from $$x = 3 to$$ $$x = 7$$?

Accepted Answer

$$2$$

Question 9

If the average rate of change of a function $$f(x)$$ from $$x = a to$$ $$x = b is $$zero, what does this indicate about the function on $$[a, b]$$?

Accepted Answer

The function has no net change between $$a$$ and $$b.$$

Question 10

Given $$f(x) = x^2$, what is the average rate of change from x = 1$ to x = 5$?

Accepted Answer

$$6$$

Question 11

A car travels such that its position at time $$t (in $$hours) is given by $$s(t) = 4t^2$ + 2t. $$What is the average velocity between $$t = 1$$ and $$t = 3$$ hours?

Accepted Answer

$$22$$ miles/hour

Question 12

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

Accepted Answer

$$-1$$

Question 13

If a function $$f(x) is $$linear, what can you say about its average rate of change between any two points?

Accepted Answer

It is constant.

Question 14

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

Accepted Answer

$$2x + h + 2$$

Question 15

A company tracks its profit $$P(x) in $$thousands of dollars, where $$x is $$the number of months since opening. If $$P(2) = 10$$ and $$P(8) = 34$$, what is the average rate of change in profit per month from month 2 to month 8?

Accepted Answer

$$3$$

Question 16

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

Accepted Answer

$$3$$

Question 17

If the graph of a function is always increasing but the average rate of change between consecutive intervals is decreasing, what does this indicate?

Accepted Answer

The function is increasing at a decreasing rate.

Question 18

Given $$f(x) = x^2$ + 2x + 1$$, what is the average rate of change from $$x = 2 to$$ $$x = 5$$?

Accepted Answer

$$13$$

Question 19

A population of bacteria is modeled by $$P(t) = 1000 + 200t$$, where $$t is in $$hours. What is the average rate of change in population from $$t = 3 to$$ $$t = 7$$?

Accepted Answer

$$200$$

Question 20

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

Accepted Answer

$$2a + h$$

B4

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