Respuesta :

calculista

Answer:

the average rate of change is equal to [tex]2[/tex]

Step-by-step explanation:

Step 1

Find the value of f(x) for [tex]x=0[/tex]

[tex]f(0)=4[/tex] ------> see the graph

Step 2

Find the value of f(x) for [tex]x=2[/tex]

[tex]f(2)=8[/tex] ------> see the graph

Step 3

Find the average rate of change f(x)

we know that

the average rate of change is equal to

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

In this problem we have

[tex]f(a)=f(0)=4[/tex]

[tex]f(b)=f(2)=8[/tex]

[tex]a=0[/tex]

[tex]b=2[/tex]

Substitute the values

[tex]\frac{8-4}{2-0}=2[/tex]

Answer:

Option 1 is correct.

2 is the average rate of change f(x), represented by the graph, over the interval [0,2]

Step-by-step explanation:

The average rate of change A(x) of f(x) over the interval [a, b] is given by:

[tex]A(x) = \frac{f(b)-f(a)}{b-a}[/tex]      .....[1]

As per the statement:

Since, the parabolic graph represents the function f(x) as shown in figure.

We have to find the average rate of change f(x), represented by the graph, over the interval [0,2]

At x = 0

From the graph, we have

f(x) = 4

At x = 2

⇒f(x) = 8

Substitute these given values in [1] we have;

[tex]A(x) = \frac{f(2)-f(0)}{2-0}[/tex]

⇒[tex]A(x) = \frac{8-4}{2-0}[/tex]

⇒[tex]A(x) = \frac{4}{2} = 2[/tex]

Therefore, the average rate of change f(x), represented by the graph, over the interval [0,2] is, 2

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