Estimate the average rate of change between x = 0 and x = 2 for the function shown.

The graph starts at the bottom left to cross the y axis at one, continues curving to the top right to cross the x axis near one point five, and continues to the top right.

A.6
B.7
C. 12
D. 24

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erinna erinna · Answer 1 · 2019-12-17T10:48:58+01:00

Answer:

Option A.

Step-by-step explanation:

Consider the below graph.

We need to find the average rate of change between x = 0 and x = 2 for the function shown.

From the given graph it is clear that the value of function at x=0 is -7 and the value of function is 5 at x=2. It means

f(0) = -7

f(2) = 5

The average rate of change of a function f(x) on [a,b] is

[tex]m=\dfrac{f(b)-f(a)}{b-a}[/tex]

The average rate of change between x = 0 and x = 2

[tex]m=\dfrac{f(2)-f(0)}{2-0}[/tex]

[tex]m=\dfrac{5-(-7)}{2-0}[/tex]

[tex]m=\dfrac{12}{2}[/tex]

[tex]m=6[/tex]

The average rate of change between x = 0 and x = 2 for the function shown is 6.

Therefore, the correct option is A.

fichoh fichoh · Answer 2 · 2021-10-29T15:16:18+02:00

The rate of change is the ratio of the rise to the run of a graph, the average rate of change between x=0 and x= 2 is 6

Using the relation :

[tex]slope, m = \frac{f(x_{1}) - f(x_{2})}{x_{1} - x_{2}} [/tex]

Substituting the values into the slope function :

[tex]slope, m = \frac{5 - - 7}{2 - 0} = \frac{12}{2} = 6[/tex]

Therefore, the average rate of change is 6

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