a. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
Students have to know the differences between linear functions and exponential functions. In simplest terms, a linear function one that takes the form y = mx + b and an exponential function is one in which y = ax.
The best way to understand these functions based on distances is to make a table of values and observe how the y values change for each increase in x. For instance, we can look at f(x) = 2x and f(x) = 2x.
If we graph the two functions, we'll see the difference between the line and the exponential. (Hint: The line is blue and the exponential is red.)