# Graph f(x) equals(x to the power of two minus four x) divide(x to the power of two minus nine)

Graph f(x)=(x^2-4x)/(x^2-9)
Find the value at .
Replace the variable with in the expression.
Simplify the result.
Reduce the expression by cancelling the common factors.
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply by .
Simplify the denominator.
Rewrite as .
Rewrite as .
Factor out of .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Simplify the denominator.
Subtract from .
Raise to the power of .
Simplify the expression.
Multiply by .
Divide by .
The final answer is .
The value at is .
Find the value at .
Replace the variable with in the expression.
Simplify the result.
Subtract from .
Simplify the denominator.
Subtract from .
Simplify the expression.
Multiply by .
Multiply by .
Move the negative in front of the fraction.
The final answer is .
The value at is .
Find the value at .
Replace the variable with in the expression.
Simplify the result.
Subtract from .
Simplify the denominator.
Multiply by .
Subtract from .
Simplify the expression.
Multiply by .
Move the negative in front of the fraction.
The final answer is .
The value at is .
Find the value at .
Replace the variable with in the expression.
Simplify the result.
Subtract from .
Simplify the denominator.
Subtract from .
Simplify the expression.
Multiply by .
Multiply by .
Divide by .
The final answer is .
The value at is .
Find the value at .
Replace the variable with in the expression.
Simplify the result.
Multiply by .
Simplify the denominator.
Subtract from .
Subtract from .
Reduce the expression by cancelling the common factors.
Multiply by .
Dividing two negative values results in a positive value.
The final answer is .
The value at is .
Find the value at .
Replace the variable with in the expression.
Simplify the result.
Subtract from .
Simplify the denominator.
Subtract from .
Reduce the expression by cancelling the common factors.
Multiply by .
Multiply by .
Dividing two negative values results in a positive value.
The final answer is .
The value at is .
List the points to graph.
Find the asymptotes.
Find where the expression is undefined.
The vertical asymptotes occur at areas of infinite discontinuity.
Consider the rational function where is the degree of the numerator and is the degree of the denominator.
1. If , then the x-axis, , is the horizontal asymptote.
2. If , then the horizontal asymptote is the line .
3. If , then there is no horizontal asymptote (there is an oblique asymptote).
Find and .
Since , the horizontal asymptote is the line where and .
There is no oblique asymptote because the degree of the numerator is less than or equal to the degree of the denominator.
No Oblique Asymptotes
This is the set of all asymptotes.
Vertical Asymptotes:
Horizontal Asymptotes:
No Oblique Asymptotes
Vertical Asymptotes:
Horizontal Asymptotes:
No Oblique Asymptotes
Use the found points and asymptotes to graph .
Vertical Asymptotes:
Horizontal Asymptotes:
No Oblique Asymptotes
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