# The Average rate of change of a function over an interval [a,b]

```Calculating & Interpreting the Average Rate of Change of Polynomials
The Average rate of change of a function y  f ( x) over an interval [a,b] is:
y f (b)  f (a )

x
ba
1) Find the average rate of change of the linear function f ( x)  3x  4 for the
interval [-2,1].
y
 _________
x
2) Using the table, Find the average rate of change of the linear function for the
interval [-2,-1] and [0,2]. Is the average rate of change the same?
x
-2
-1
0
2
y
2
-1
-4
-10
3) The table below shows the elapsed time when two different cars pass a
10,20,30,40 and 50 meter on a test track.
a) For car 1, what is the average velocity between the 0 and 10 meter mark?
Between the 0 and 50 mark? Between the 20 and 30 meter mark? Analyze
the data to describe the motion of the car 1.
b) How does the velocity of car 1 compare to
that of car 2?
d
10
20
30
40
50
Car 1
t
4.472
6.325
7.746
8.944
10
Car 2
t
1.742
2.899
3.831
4.633
5.348
Calculating & Interpreting the Average Rate of Change of Polynomials
4) Find the average rate of change of f ( x)  ( x  3)2
a)
Interval [1,3]
_______
b)
Interval [4,7]. _______
c)
Compare & contrast the two average
rates of change.
5) The value of an antique has increased exponentially, as shown in this graph.
Based on the graph, estimate to the
nearest \$50 the average rate of
change for the following time
intervals.
From 0 to 20 years: _________
From 20 to 40 years: _________
Calculating & Interpreting the Average Rate of Change of Polynomials
6) Find the average rate of change of the following the function over intervals:
a) [-2,-1]
b) 2  x  1
c) From x  2 to x  1
d) Compare and contrast
these intervals.
7) Find the average rate of change of the following intervals from the graph above.
a) [-2,-1]
b) [-1, 2]
c) [2, 3]
d) Compare and contrast
these intervals.
```
Linear algebra

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Abstract algebra

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