Question

The function y=f(x) is graphed below. Plot a line segment connecting the points on f where x=−3 and x=6. Use the line segment to determine the average rate of change of the function f(x) on the interval −3≤x≤6.

Answer 1

Step-by-step explanation

Plotting the line segment:

Now, we need to compute the slope in order to get the average rate of change, by taking two ordered pairs, as for instance, (x_1,y_1)=(-3,10) and

(x_2,y_2) = (6,-10)

`Slope=(y_2-y_1)/(x_2-x_1)`

Plugging in the terms into the expression:

`Slope=(-10-10)/(6-(-3))`

Subtracting numbers:

`Slope=(-20)/(8)`

Simplifying:

`Slope=-(5)/(2)`

The average rate of change is -5/2