Answer:
-3/2
Step-by-step explanation:
The average rate of change is synonymous to the slope.
So, to find the average rate of change from the interval x=-2 to x=2, first find the y-values at x=-2 and x=2.
At x=-2, we can see that y is 4. Thus, we have (-2,4).
At x=2, we can see that y is -2. Thus, we have (2,-2).
Now, use the slope formula. The formula for slope is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let (-2,4) be x₁ and y₁ and let (2,-2) be x₂ and y₂. Therefore:
[tex]m=\frac{-2-4}{2--2}[/tex]
Simplify:
[tex]m=\frac{-6}{4}[/tex]
Reduce:
[tex]m=-3/2[/tex]
So, our average rate of change from the interval x=-2 to x=2 is -3/2.
