Question

The graph below plots a function f(x):

If x represents time, the average rate of change of the function f(x) in the first three
seconds is....

Answer 1

-50

Explanation:

The average rate of change is synonymous with the slope. Therefore, we will find the slope of the function from x=0 to x=3.

So, we will use the endpoints of the function.

At x=0, f(x)=150. Thus, we have the point (0, 150).

At x=3, f(x)=0. Thus, we have the point (3, 0).

Now, we can use the slope formula:

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

Let (0, 150) be (x₁, y₁) and let (3, 0) be (x₂, y₂). Substitute:

`m=(0-150)/(3-0)=-150/3=-50`

Therefore, the average rate of change for the first three seconds is -50.