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This printable supports Common Core Mathematics Standard HSF-IF.B.6

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# Average Rate of Change (Grade 10)

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## Average Rate of Change

1.
Find the average rate of change of $g(x)=x^2-5$ from -3 to 2.
1. $3/5$
2. $-1$
3. $14$
4. $-13/5$
2.
Find the average rate of change of $r(x)=x^3-2x+1$ from 1 to 3.
1. 11
2. 2
3. 10
4. 17
3.
Find the average rate of change from x = 0 to x = 3 for the following function.
$f(x)=x^2+5x$
1. 8
2. 0
3. -4
4. 6
4.
What is the average rate of change between x = 0 and x = 2? Assume 1 unit intervals for both axes.
1. 2/3
2. 3/2
3. 2
4. 1/2
5.
What is the average rate of change between $x=-1$ and $x=2$ for the following function? Assume 1 unit intervals for both axes.
1. $1/6$
2. $3/2$
3. $2/3$
4. $0$
6.
What is the average rate of change between $x=-3$ and $x=-1 ?$ Assume the horizontal axis represents x and the vertical axis represents y.
1. $-4$
2. $-1/2$
3. $-2$
4. $1$
7.
Given the function values listed in the table below, what is the average rate of change for $f(x)$ between $x=0.5$ and $x=1.5 ?$

 $\ \ \ \ \mathbf{x} \ \ \ \$ $\ \ \ \ \mathbf{f(x)} \ \ \ \$ $0$ $-1.00$ $0.5$ $1.92$ $1$ $1.30$ $1.5$ $0.95$ $2$ $0.74$ $2.5$ $0.61$
1. 1.00
2. -0.97
3. 0
4. -0.03
8.
Jonathan is doing research into marine life in a small lake. He has recorded the number of frogs at the lake on the first day of each month, for one year. He is most interested in the average population increase from March to May. What is this value, rounded to the nearest unit?

 $\ \ \ \ mathbf{"Month"} \ \ \ \$ $"Jan."$ $"Feb."$ $"Mar."$ $"Apr."$ $"May"$ $"June"$ $"July"$ $"Aug."$ $"Sept."$ $"Oct."$ $"Nov."$ $"Dec."$ $\ \ \ \ \mathbf{"Frog Population"} \ \ \ \$ $90$ $90$ $95$ $110$ $120$ $150$ $160$ $160$ $162$ $130$ $135$ $130$
1. 13 frogs per month
2. 60 frogs per month
3. 48 frogs per month
4. 25 frogs per month
9.
Marsha has just poured a cup of tea. The function $T(t) = 73 + 139 e^(-0.05t)$ will give the temperature of the tea, in degrees Fahrenheit, after t minutes. When will the tea cool most rapidly? In the first 5 minutes, between 5 and 10 minutes, between 10 and 15 minutes, or between 15 and 20 minutes after pouring?
1. The first 5 minutes.
2. Between 5 and 10 minutes.
3. Between 10 and 15 minutes.
4. Between 15 and 20 minutes.
10.
A small shop at the mall wraps presents during the holidays. Over the past few years, they have kept track of the number of workers they have on hand and the number of presents they are able to wrap in an hour. The following table represents this data.

 $\ \ \ \ "Number of Workers" \ \ \ \$ $\ \ \ \ "Number of Presents Wrapped per Hour" \ \ \ \$ $5$ $24$ $6$ $28$ $7$ $33$ $8$ $40$ $9$ $44$ $10$ $46$

If this year they currently have 7 workers, what would be the most productive number of additional employees to hire, and why?
1. 0, because they are already wrapping presents as efficiently as they can.
2. 3, since this would mean the most presents wrapped in an hour.
3. 2, since this would be the largest average increase possible (the most additional presents wrapped for each worker hired).
4. 1, because this would be the largest average increase possible (the most additional presents wrapped for each worker hired).
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