Question

Which is the best interpretation of the averagerate of change of this function?

Answer 1

We can calculate the rate of change as the slope between two points, like (1,2) and (2,4).

The slope is:

`m=(y_2-y_1)/(x_2-x_1)=(4-2)/(2-1)=(2)/(1)=2`

If this is a linear function, this slope m has to be constant.

We will calculate the slope between other points, like (3,8) and (4,16):

`m=(y_4-y_3)/(x_4-x_3)=(16-8)/(4-3)=(8)/(1)=8`

The slope is not constant, so this function is not a linear function.

If we look at how f(x) increases, we can prove that f(x) is:

`f(x)=2^x`

and this function is an exponential function.

Answer: Option B (exponential function).