Answer: [tex]average\ rate\ of\ change\approx-3[/tex]
Step-by-step explanation:
For this exercise you need to use the following formula:
[tex]average\ rate\ of\ change=\frac{f(b)-f(a)}{b-a}[/tex]
You need to find the average rate of change of the given function g(x) over the following interval:
[tex][-1,2][/tex]
So, you can see in the table that the point whose x-coordinate is -1, is:
[tex](-1,5)[/tex]
And the point whose x-coordinate is 2, is:
[tex](2,-3)[/tex]
Knowing this, let be:
[tex]a=-1\\f(a)=5\\\\b=2\\f(b)=-3[/tex]
Now you can substitute values into the formula:
[tex]average\ rate\ of\ change=\frac{-3-5}{2-(-1)}[/tex]
Finally, evaluating, you get that the average rate of change over the interval indicated in the exercise, is:
[tex]average\ rate\ of\ change=\frac{-8}{3}\\\\average\ rate\ of\ change=-2.66\\\\average\ rate\ of\ change\approx-3[/tex]
