Question

The graph of f(x) = 2^x + 1 is shown below. Explain how to find the average rate of change between x = 0 and x = 2.

Answer 1

$\bf slope = \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{f(x_2)-f(x_1)}{x_2-x_1}\impliedby \begin{array}{llll} \textit{average rate}\\ \textit{of change} \end{array} \\\\\\ f(x)=2^{x}+1\quad \begin{cases} x_1=0\\ x_2=2 \end{cases}\implies \cfrac{f(x_2)-f(x_1)}{x_2-x_1}\implies \cfrac{(2^{2}+1)-(2^{0}+1)}{2-0}$

just to point out, you didn't include the graph, in this case, it doesn't matter much, that's not the case most times... just so you know