Question

Consider the graph of function f. Find the average rate of change for f on the interval [P,Q]

Answer 1

Check the picture below.

$\bf slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array}\\\\[-0.35em] \rule{31em}{0.25pt}\\\\ f(x)= \qquad \begin{cases} x_1=1\\ x_2=3 \end{cases}\implies \cfrac{f(3)-f(1)}{3-1}\implies \cfrac{(5)-(-1)}{3-1} \\\\\\ \cfrac{5+1}{2}\implies \cfrac{6}{2}\implies 3$