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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

What is the functions average rate of change over each intervala x 3 to x 2b x 2 to x 1c x 0 to x 1d x 1 to x 2e x 1 to x 0f x 1 to x 2 class=

Respuesta :

we can use average rate of change formula

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

(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

[tex]=\frac{2-0}{-2+3}[/tex]

[tex]=2[/tex]

(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

[tex]=\frac{-4-2}{1+2}[/tex]

[tex]=-2[/tex]

(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

[tex]=\frac{-4+3}{1-0}[/tex]

[tex]=-1[/tex]

(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

[tex]=\frac{0+4}{2-1}[/tex]

[tex]=4[/tex]

(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

[tex]=\frac{-3-0}{0+1}[/tex]

[tex]=-3[/tex]


(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

[tex]=\frac{0-0}{2+1}[/tex]

[tex]=0[/tex]


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