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.

`(df(x))/(dx)=(\Delta y)/(\Delta x)`

sames apply for g(x)

use the formula for f(x)

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

do the same for g(X)

`\begin{gathered} (dg(x))/(dx)=(g(x2)-g(x1))/(x2-x1) \\ =(5-(-2))/(12-5) \\ =(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.