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.

1)  calculate f(3), that means substituting the x in the formula, by the number 3.
f(3) = 2^x + 1
f(3)= 2^3 + 1
f(3) =9  You don't even need to calculate it. Just by looking at the graph you see that when x=3 the "blue line" will match with y=9

2)calculate f(1), that means substituting the x in the formula, by the number 1.
f(1) = 2^x + 1
f(1)= 2^1 + 1
f(1) =3      Just by looking at the graph you see that when x=1 the "blue line" will match with y=3.
3) To calculate the average rate of change, you need to follow a formula. (b is 3 and a is 1)
[tex] \frac{f(b)-f(a)}{b-a} [/tex]
[tex] \frac{f(3)-f(1)}{3-1} [/tex]