Answered

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Examine the graph of f(x) and the table that contains values of g(x). Curve f of x approaches Y equals negative 7 on the left and positive infinity on the right. It passes through points (0, negative 4) and (1, 2).© 2018 StrongMind. Created using GeoGebra. x g(x) −1 1 0 3 1 9 2 27 3 81 Which function has a greater average rate of change over the interval 0≤x≤1?

Examine The Graph Of Fx And The Table That Contains Values Of Gx Curve F Of X Approaches Y Equals Negative 7 On The Left And Positive Infinity On The Right It P class=

Sagot :

Answer:

The correct answer is the last option: " Both functions have the same average rate of change over this interval"

Explanation:

If we are given a function h(x), and we want to know the average rate of change in an interval [a, b], we use the formula:

[tex]Average\text{ }rate\text{ }of\text{ }change=\frac{h(a)-h(b)}{a-b}[/tex]

In this case, we are looking the interval [0, 1].

In the graph for f(x), we can see:

f(0) = -4

f(1) = 2

The average change of rate of f(x) in [0, 1] is:

[tex]\frac{f(0)-f(1)}{0-1}=\frac{-4-2}{0-1}=\frac{-6}{-1}=6[/tex]

In the table for g(x), we can see:

g(0) = 3

g(1) = 9

The average rate of change of g(x) in [0, 1 ] is:

[tex]\frac{g(0)-g(1)}{0-1}=\frac{3-9}{0-1}=\frac{-6}{-1}=6[/tex]

Thus, the average rate of change of both functions is the same in [0, 1]

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