Precalculus Examples

f(x)=3x+3f(x)=3x+3 , x=3x=3
Step 1
Consider the difference quotient formula.
f(x+h)-f(x)hf(x+h)f(x)h
Step 2
Find the components of the definition.
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Step 2.1
Evaluate the function at x=x+hx=x+h.
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Step 2.1.1
Replace the variable xx with x+hx+h in the expression.
f(x+h)=3(x+h)+3f(x+h)=3(x+h)+3
Step 2.1.2
Simplify the result.
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Step 2.1.2.1
Apply the distributive property.
f(x+h)=3x+3h+3f(x+h)=3x+3h+3
Step 2.1.2.2
The final answer is 3x+3h+33x+3h+3.
3x+3h+33x+3h+3
3x+3h+33x+3h+3
3x+3h+33x+3h+3
Step 2.2
Reorder 3x3x and 3h3h.
3h+3x+33h+3x+3
Step 2.3
Find the components of the definition.
f(x+h)=3h+3x+3f(x+h)=3h+3x+3
f(x)=3x+3f(x)=3x+3
f(x+h)=3h+3x+3f(x+h)=3h+3x+3
f(x)=3x+3f(x)=3x+3
Step 3
Plug in the components.
f(x+h)-f(x)h=3h+3x+3-(3x+3)hf(x+h)f(x)h=3h+3x+3(3x+3)h
Step 4
Simplify.
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Step 4.1
Simplify the numerator.
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Step 4.1.1
Factor 33 out of 3x+33x+3.
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Step 4.1.1.1
Factor 33 out of 3x3x.
3h+3x+3-(3(x)+3)h3h+3x+3(3(x)+3)h
Step 4.1.1.2
Factor 3 out of 3.
3h+3x+3-(3(x)+3(1))h
Step 4.1.1.3
Factor 3 out of 3(x)+3(1).
3h+3x+3-(3(x+1))h
3h+3x+3-13(x+1)h
Step 4.1.2
Multiply -1 by 3.
3h+3x+3-3(x+1)h
Step 4.1.3
Factor 3 out of 3h+3x+3-3(x+1).
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Step 4.1.3.1
Factor 3 out of 3h.
3h+3x+3-3(x+1)h
Step 4.1.3.2
Factor 3 out of 3x.
3h+3(x)+3-3(x+1)h
Step 4.1.3.3
Factor 3 out of 3.
3h+3(x)+3(1)-3(x+1)h
Step 4.1.3.4
Factor 3 out of -3(x+1).
3h+3(x)+3(1)+3(-(x+1))h
Step 4.1.3.5
Factor 3 out of 3h+3(x).
3(h+x)+3(1)+3(-(x+1))h
Step 4.1.3.6
Factor 3 out of 3(h+x)+3(1).
3(h+x+1)+3(-(x+1))h
Step 4.1.3.7
Factor 3 out of 3(h+x+1)+3(-(x+1)).
3(h+x+1-(x+1))h
3(h+x+1-(x+1))h
Step 4.1.4
Apply the distributive property.
3(h+x+1-x-11)h
Step 4.1.5
Multiply -1 by 1.
3(h+x+1-x-1)h
Step 4.1.6
Subtract x from x.
3(h+0+1-1)h
Step 4.1.7
Add h and 0.
3(h+1-1)h
Step 4.1.8
Subtract 1 from 1.
3(h+0)h
Step 4.1.9
Add h and 0.
3hh
3hh
Step 4.2
Cancel the common factor of h.
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Step 4.2.1
Cancel the common factor.
3hh
Step 4.2.2
Divide 3 by 1.
3
3
3
Step 5
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