Question

given the function g(x)=x^2+5x-2 determine the average rate of change of the function over the interval -9 ≤ x ≤ 3​

Answer 1

The average rate of change over an interval is the same as the slope between those two values.  The formulate for slope is:

$m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}$

You are given the x values: x2=3 and x1=-9.  Plug in these x values to g(x) find the y values:

g(3)=3^2+5(3)-2=9+15-2=22

g(-9)=(-9)^2+5(-9)-2=81-45-2=34

Now, you can solve for m:

m=(22-34)/(3--9)

m=-12/12

m=1

Hope this helps!!