Trigonometry Examples

Graph f(x) = log of 14-x+ log of x-5
Step 1
Find the asymptotes.
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Step 1.1
Set the argument of the logarithm equal to zero.
Step 1.2
Solve for .
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Step 1.2.1
Factor the left side of the equation.
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Step 1.2.1.1
Factor out of .
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Step 1.2.1.1.1
Reorder the expression.
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Step 1.2.1.1.1.1
Move .
Step 1.2.1.1.1.2
Reorder and .
Step 1.2.1.1.2
Factor out of .
Step 1.2.1.1.3
Factor out of .
Step 1.2.1.1.4
Rewrite as .
Step 1.2.1.1.5
Factor out of .
Step 1.2.1.1.6
Factor out of .
Step 1.2.1.2
Factor.
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Step 1.2.1.2.1
Factor using the AC method.
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Step 1.2.1.2.1.1
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Step 1.2.1.2.1.2
Write the factored form using these integers.
Step 1.2.1.2.2
Remove unnecessary parentheses.
Step 1.2.2
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 1.2.3
Set equal to and solve for .
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Step 1.2.3.1
Set equal to .
Step 1.2.3.2
Add to both sides of the equation.
Step 1.2.4
Set equal to and solve for .
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Step 1.2.4.1
Set equal to .
Step 1.2.4.2
Add to both sides of the equation.
Step 1.2.5
The final solution is all the values that make true.
Step 1.3
The vertical asymptote occurs at .
Vertical Asymptote:
Vertical Asymptote:
Step 2
The log function can be graphed using the vertical asymptote at and the points .
Vertical Asymptote:
Step 3