Question

35 POINTS! The table below shows the function f.

Answer 1

$\bf slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array}\\\\[-0.35em] \rule{31em}{0.25pt}\\\\ \begin{array}{|c|ccccc|} \cline{1-6} x&2&3&4&5&6\\ f(x)&z&15&23&39&71 \\ \cline{1-6} \end{array} \qquad \qquad \begin{cases} x_1=2\\ x_2=6 \end{cases}\implies \cfrac{f(6)-f(2)}{6-2}=15 \\\\\\ \cfrac{71-z}{4}=15\implies 71-z=60\implies 11=\stackrel{f(2)}{z}$