Precalculus Examples

Find the Average Rate of Change y=(x+2)^2
Step 1
Write as a function.
Step 2
Consider the difference quotient formula.
Step 3
Find the components of the definition.
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Step 3.1
Evaluate the function at .
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Step 3.1.1
Replace the variable with in the expression.
Step 3.1.2
Simplify the result.
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Step 3.1.2.1
Rewrite as .
Step 3.1.2.2
Expand by multiplying each term in the first expression by each term in the second expression.
Step 3.1.2.3
Simplify each term.
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Step 3.1.2.3.1
Multiply by .
Step 3.1.2.3.2
Move to the left of .
Step 3.1.2.3.3
Multiply by .
Step 3.1.2.3.4
Move to the left of .
Step 3.1.2.3.5
Multiply by .
Step 3.1.2.4
Add and .
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Step 3.1.2.4.1
Reorder and .
Step 3.1.2.4.2
Add and .
Step 3.1.2.5
Add and .
Step 3.1.2.6
Add and .
Step 3.1.2.7
The final answer is .
Step 3.2
Reorder.
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Step 3.2.1
Move .
Step 3.2.2
Reorder and .
Step 3.3
Find the components of the definition.
Step 4
Plug in the components.
Step 5
Simplify.
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Step 5.1
Simplify the numerator.
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Step 5.1.1
Apply the distributive property.
Step 5.1.2
Simplify.
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Step 5.1.2.1
Multiply by .
Step 5.1.2.2
Multiply by .
Step 5.1.3
Subtract from .
Step 5.1.4
Add and .
Step 5.1.5
Subtract from .
Step 5.1.6
Add and .
Step 5.1.7
Subtract from .
Step 5.1.8
Add and .
Step 5.1.9
Factor out of .
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Step 5.1.9.1
Factor out of .
Step 5.1.9.2
Factor out of .
Step 5.1.9.3
Factor out of .
Step 5.1.9.4
Factor out of .
Step 5.1.9.5
Factor out of .
Step 5.2
Reduce the expression by cancelling the common factors.
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Step 5.2.1
Cancel the common factor of .
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Step 5.2.1.1
Cancel the common factor.
Step 5.2.1.2
Divide by .
Step 5.2.2
Reorder and .
Step 6