Precalculus Examples

Find the Average Rate of Change f(x) = square root of x-x+1
Step 1
Consider the difference quotient formula.
Step 2
Find the components of the definition.
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Step 2.1
Evaluate the function at .
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Step 2.1.1
Replace the variable with in the expression.
Step 2.1.2
Simplify the result.
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Step 2.1.2.1
Remove parentheses.
Step 2.1.2.2
Apply the distributive property.
Step 2.1.2.3
The final answer is .
Step 2.2
Reorder.
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Step 2.2.1
Reorder and .
Step 2.2.2
Move .
Step 2.2.3
Reorder and .
Step 2.3
Find the components of the definition.
Step 3
Plug in the components.
Step 4
Simplify.
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Step 4.1
Simplify the numerator.
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Step 4.1.1
Apply the distributive property.
Step 4.1.2
Simplify.
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Step 4.1.2.1
Multiply .
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Step 4.1.2.1.1
Multiply by .
Step 4.1.2.1.2
Multiply by .
Step 4.1.2.2
Multiply by .
Step 4.1.3
Add and .
Step 4.1.4
Add and .
Step 4.1.5
Subtract from .
Step 4.1.6
Add and .
Step 4.2
Simplify with factoring out.
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Step 4.2.1
Factor out of .
Step 4.2.2
Factor out of .
Step 4.2.3
Factor out of .
Step 4.2.4
Factor out of .
Step 4.2.5
Simplify the expression.
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Step 4.2.5.1
Rewrite as .
Step 4.2.5.2
Move the negative in front of the fraction.
Step 5