Precalculus Examples

Find the Average Rate of Change table[[x,y],[-2,1/5],[-1,1],[0,5],[1,25],[2,125]]
Step 1
Choose the starting and ending values from the table.
Step 2
To find the average rate of change, find the slope.
Step 3
Slope is equal to the change in over the change in , or rise over run.
Step 4
The change in is equal to the difference in x-coordinates (also called run), and the change in is equal to the difference in y-coordinates (also called rise).
Step 5
Substitute in the values of and into the equation to find the slope.
Step 6
Simplify.
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Step 6.1
Multiply the numerator and denominator of the fraction by .
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Step 6.1.1
Multiply by .
Step 6.1.2
Combine.
Step 6.2
Apply the distributive property.
Step 6.3
Cancel the common factor of .
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Step 6.3.1
Move the leading negative in into the numerator.
Step 6.3.2
Cancel the common factor.
Step 6.3.3
Rewrite the expression.
Step 6.4
Simplify the numerator.
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Step 6.4.1
Multiply by .
Step 6.4.2
Subtract from .
Step 6.5
Simplify the denominator.
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Step 6.5.1
Multiply by .
Step 6.5.2
Multiply .
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Step 6.5.2.1
Multiply by .
Step 6.5.2.2
Multiply by .
Step 6.5.3
Add and .
Step 6.6
Cancel the common factor of and .
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Step 6.6.1
Factor out of .
Step 6.6.2
Cancel the common factors.
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Step 6.6.2.1
Factor out of .
Step 6.6.2.2
Cancel the common factor.
Step 6.6.2.3
Rewrite the expression.
Step 7