Question

Select the correct function. Select the function with an average rate of change of 3 over the interval [1, 3].

Answer 1

Answer:

Function g(x)

Step-by-step explanation:

Given

See attachment for functions

Required

Which has an average rate of 3 over [1,3]

The average rate of change (m) is calculated as:

$m = \frac{f(b) - f(a)}{b -a}$

Where:

$[a,b] = [1,3]$

So, we have:

$m = \frac{f(3) - f(1)}{3 -1}$

$m = \frac{f(3) - f(1)}{2}$

From the table f(x), we have:

$f(3) = 6\\ f(1) = -2$

So:

$m = \frac{6 - -2}{2}$

$m = \frac{8}{2}$

$m =4$

From the graph of g(x), we have:

$g(3) = 4\\ g(1) = -2$

So:

$m = \frac{g(3) - g(1)}{2}$

$m = \frac{4 - -2}{2}$

$m = \frac{6}{2}$

$m =3$

Since only one of the function has an average rate of change of 3 over the given interval,

Then g(x) answers the question