Precalculus Examples

Find the Average Rate of Change y=- square root of x-1+5
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
Remove parentheses.
Step 3.1.2.2
The final answer is .
Step 3.2
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
Multiply .
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Step 5.1.2.1
Multiply by .
Step 5.1.2.2
Multiply by .
Step 5.1.3
Multiply by .
Step 5.1.4
Subtract from .
Step 5.1.5
Add and .
Step 5.2
Simplify with factoring out.
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Step 5.2.1
Factor out of .
Step 5.2.2
Factor out of .
Step 5.2.3
Simplify the expression.
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Step 5.2.3.1
Rewrite as .
Step 5.2.3.2
Move the negative in front of the fraction.
Step 6