Question

The graph of f(x) = 2x + 1 is shown below. Explain how to find the average rate of change between x = 1 and x = 3.

Graph of 2 to the power of x plus 1

Answer 1

So we got the function of the graph f(x) = 2^x + 1 what you will need to do first is find the y-coordinates corresponding to x=1 and x=3 which can be found by substituting into the function. After that we can find the average rate of change using y2-y1/x2-x1.

f(1)=2^1+1 which would be equal to 3

1,3

f(3)=2^3+1 which would be equal to 9

3,9

9-3/3-1=6/2

6/2=3

The average rate of change is 3.