Question
Asked Oct 4, 2019
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A function is given. 

g(x) = 4/(x+7); x=0, x=h

(a) Determine the net change between the given values of the variable.

(b) Determine the average rate of change between the given values of the variable.

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Expert Answer

Step 1

Given a function:

4
g(x)
x7X= 0 and x = h_
To determine:
a) The net change between the given values of the variable
b) The average rate of change between the given values of the variable
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4 g(x) x7X= 0 and x = h_ To determine: a) The net change between the given values of the variable b) The average rate of change between the given values of the variable

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Step 2

We begin with finding the net change of g(x):

Note: Let f (x) be a function continuous on an interval containing a and b with a < b. The net change of f (x) as x
increases from a to b is the difference f (b) – f (a).

So, the net change = g(h) - g(0)
4
4
h+7
4
0+7
h+7
7
(7-(h+7)
4
7 (h+7)
7 - h 7)
= 4
7(h7)
-4h
7(h+7)
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So, the net change = g(h) - g(0) 4 4 h+7 4 0+7 h+7 7 (7-(h+7) 4 7 (h+7) 7 - h 7) = 4 7(h7) -4h 7(h+7)

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Step 3

Now, we find the Average ra...

Note: The formula for average change is given by:
Average rate of change = Change in y
Change in x
g(h)-g(0)
h-0
-4h
7(h+7)
. (the numerator is the net change)
h
-4
7(h+7)
help_outline

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Note: The formula for average change is given by: Average rate of change = Change in y Change in x g(h)-g(0) h-0 -4h 7(h+7) . (the numerator is the net change) h -4 7(h+7)

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