Question

What is the average rate of change from x = 2 to x = 3?

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Answer 1

So, the *average* rate of change is:

(y_final-y_start)/(x_final-x_start) (also for physics!)

In your case:

average rate of change is:

(-1-(-3))/(3-2) = 2/1=2

You can see it's +, so increasing (yeah).

if you would make the interval very small, from x=2 to x=2.00001, and so n, you'd get the concept of slope and derivative (but that's just to let u know)

Answer 2

The average rate of change from x = 2 to x = 3 is 2. Therefore first option is correct.

Explanation:

The average rate of a function f(x) on the interval [a,b] is defined as

`m=(f(b)-f(a))/(b-a)`

The average rate of change from x = 2 to x = 3 is

`m=(f(3)-f(2))/(3-2)` .... (1)

From the given graph it is clear that the value of the function is -3 at x=2 and -1 at x=3. It means f(2)=-3 and f(3)=-1.

Put f(2)=-3 and f(3)=-1 in equation (1).

`m=(-1-(-3))/(3-2)`

`m=(-1+3)/(1)`

`m=(2)/(1)`

`m=2`

The average rate of change from x = 2 to x = 3 is 2. Therefore first option is correct.