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Find the average rate of change of each function over the interval [0, 3]. Match each representation with its respective average rate of change.
3
-2
5
-1
6
-3

Sagot :

The average rate of change is illustrated below.

How to illustrate the average rate?

The average rate of change over interval [a,b]: r=[f(b)-f(a)]/(b-a).

In this case the interval is [0,2], then a=0, b=2

r=[f(2)-f(0)]/(2-0)

r=[f(2)-f(0)]/2

1) First function: h(x)

r=[h(2)-h(0)]/2

x=2→h(2)=(2)^2+2(2)-6

h(2)=4+4-6

h(2)=2

x=0→h(0)=(0)^2+2(0)-6

h(0)=0+0-6

h(0)=-6

r=[h(2)-h(0)]/2

r=[2-(-6)]/2

r=(2+6)/2

r=(8)/2

r=4

2) Second function: f(x)

A function, f, has an

x-intercept at (2,0)→x=2, f(2)=0

and a y-intercept at (0,-10)→x=0, f(0)=-10

r=[f(2)-f(0)]/2

r=[0-(-10)]/2

r=(0+10)/2

r=(10)/2

r=5

3) Third function: g(x)

r=[g(2)-g(0)]/2

From the graph:

g(2)=6

g(0)=2

r=(6-2)/2

r=(4)/2

r=2

4) Fourth function: j(x)

r=[j(2)-j(0)]/2

From the table:

x=2→j(2)=-8

x=0→j(0)=4

r=(-8-4)/2

r=(-12)/2

r=-6

Learn more about average rate on:

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