Suppose that \(f\) is the function given by the graph below and that \(a\) and \(a+h\) are the input values as labeled on the \(x\)-axis. Use the graph in Figure 1.3.2 to answer the following questions.
Construct a right triangle whose hypotenuse is the line segment from \((a,f(a))\) to \((a+h,f(a+h))\text{.}\) What are the lengths of the respective legs of this triangle?
Write a meaningful sentence that explains how the average rate of change of the function on a given interval and the slope of a related line are connected.
