Question

the table shows the values for the function f(x) and g(x) which function has the greater rate of change over the interval is [5,12]a) f(x)b) g(x)c) the rates varyd) the rates are equalsorry I forgot to include the table last time

Answer 1

to calculate the rate of change for ecah function we use the definition.

$\frac{df(x)}{dx}=\frac{\Delta y}{\Delta x}$

sames apply for g(x)

use the formula for f(x)

$\begin{gathered} \frac{df(x)}{dx}=\frac{f(x2)-f(x1)}{x2-x1} \\ =\frac{8-(-1)}{12-5} \\ =\frac{9}{7}\approx1.29 \end{gathered}$

do the same for g(X)

$\begin{gathered} \frac{dg(x)}{dx}=\frac{g(x2)-g(x1)}{x2-x1} \\ =\frac{5-(-2)}{12-5} \\ =\frac{7}{7}=1 \end{gathered}$

compare the rates and see which one is bigger.

$1.29>1$

The function f(x) has a greater rate.