Question

What is the functions average rate of change over each interval?

a. x = -3 to x = -2
b. x = -2 to x = 1
c. x = 0 to x = 1
d. x = 1 to x = 2
e. x = -1 to x = 0
f. x = -1 to x = 2

Answer 1

we can use average rate of change formula

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

(a) x = -3 to x = -2

Firstly, we will find points

(-3, 0) and (-2,2)

now, we can plug these values into formula

and we get

`=(2-0)/(-2+3)`

`=2`

(b)x = -2 to x =1

Firstly, we will find points

(-2,2) and (1,-4)

now, we can plug these values into formula

and we get

`=(-4-2)/(1+2)`

`=-2`

(c) x = 0 to x =1

Firstly, we will find points

(0,-3) and (1,-4)

now, we can plug these values into formula

and we get

`=(-4+3)/(1-0)`

`=-1`

(d) x = 1 to x =2

Firstly, we will find points

(1,-4) and (2,0)

now, we can plug these values into formula

and we get

`=(0+4)/(2-1)`

`=4`

(e) x = -1 to x =0

Firstly, we will find points

(-1,0) and (0,-3)

now, we can plug these values into formula

and we get

`=(-3-0)/(0+1)`

`=-3`

(f) x = -1 to x =2

Firstly, we will find points

(-1,0) and (2,0)

now, we can plug these values into formula

and we get

`=(0-0)/(2+1)`

`=0`