# Find the Symmetry f(x)=(x^2+x-6)/(x-4) Determine if the function is odd, even, or neither in order to find the symmetry.
1. If odd, the function is symmetric about the origin.
2. If even, the function is symmetric about the y-axis.
Find .
Find by substituting for all occurrence of in .
Remove parentheses.
Simplify the numerator.
Let . Substitute for all occurrences of .
Apply the product rule to .
Raise to the power of .
Multiply by .
Factor using the AC method.
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 .
Write the factored form using these integers.
Replace all occurrences of with .
Simplify with factoring out.
Factor out of .
Rewrite as .
Factor out of .
Rewrite negatives.
Rewrite as .
Move the negative in front of the fraction.
A function is even if .
Check if .
Since , the function is not even.
The function is not even
The function is not even
A function is odd if .
Factor using the AC method.
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 .
Write the factored form using these integers.
Since , the function is not odd.
The function is not odd
The function is not odd
The function is neither odd nor even
Since the function is not odd, it is not symmetric about the origin.
No origin symmetry
Since the function is not even, it is not symmetric about the y-axis.
No y-axis symmetry
Since the function is neither odd nor even, there is no origin / y-axis symmetry.
Function is not symmetric
Find the Symmetry f(x)=(x^2+x-6)/(x-4)