Given the function f(x) = 5x, section a is from x = 0 to x = 1 and section b is from x = 2 to x = 3. part a: find the average rate of change of each section. (4 points) part b: how many times greater is the average rate of change of section b than section a? explain why one rate of change is greater than the other

Section A :

First you need to find the y values.

Plug x = 0 into the equation you will get f(0)=0

Plug x = 1 into the equation you will get f(1)=5

Recall that the rate of change ( slope ) formula is :

( y2 - y1) /( x2 - x1 )

Now execute the slope :

(5-0)/(1-0) = 5.

So the rate of change for the first Section is 5.

Section B :

First you need to find the y values.

Plug x = 2 into the equation you will get f(2)=10

Plug x = 3 into the equation you will get f(3)=15

Now execute the slope :

(15-10)/(3-2) = 5.

So the rate of change for the Section B is also 5.

The rate of change for the both of sections are the same. The reason of that is because it's a Proportional Relationship which means that y varies directly as x if :

y=kx => where k is a constant.

This means that as x increases,y increases and as x decreases, y decreases and that the ratio between them always stays the same.

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