SOLUTION: Determine whether the rational function has symmetry with respect to the origin, symmetry with respect to the y-axis, or neither. f(x) = -9x^2-9x-10/7x+7 a. symmetry with r

Algebra ->  Graphs -> SOLUTION: Determine whether the rational function has symmetry with respect to the origin, symmetry with respect to the y-axis, or neither. f(x) = -9x^2-9x-10/7x+7 a. symmetry with r      Log On


   

Question 1042742: Determine whether the rational function has symmetry with respect to the origin, symmetry with respect to the y-axis, or neither.
f(x) = -9x^2-9x-10/7x+7
a. symmetry with respect to the origin
b. symmetry with respect to the y-axis
c. neither
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+%28-9x%5E2-9x-10%29%2F%287x%2B7%29


f%28-x%29+=+%28-9%28-x%29%5E2-9%28-x%29-10%29%2F%287%28-x%29%2B7%29 Replace every 'x' with '-x'


f%28-x%29+=+%28-9x%5E2%2B9x-10%29%2F%28-7x%2B7%29


We can see that f(x) and f(-x) are two completely different functions.


So f(x) is NOT even.


This means the function does NOT have symmetry with respect to the y axis.


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f%28x%29+=+%28-9x%5E2-9x-10%29%2F%287x%2B7%29


-1%2Af%28x%29+=+-1%2A%28%28-9x%5E2-9x-10%29%2F%287x%2B7%29%29 Multiply both sides by -1


-f%28x%29+=+%28-1%28-9x%5E2-9x-10%29%29%2F%287x%2B7%29


-f%28x%29+=+%289x%5E2%2B9x%2B10%29%2F%287x%2B7%29


We can see that f(-x) and -f(x) are two completely different functions.


So f(x) is NOT odd.


This means the function does NOT have symmetry with respect to the origin.


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The final answer is choice C) Neither.