SOLUTION: Wondering if I am heading in the right direction. My question is: Is f(x)=x^1171 - 5x^109 + 3 y-axis symmetric, origin symmetric or neither. When I plug (-x) into the e

Question 214835: Wondering if I am heading in the right direction. My question is:
Is f(x)=x^1171 - 5x^109 + 3 y-axis symmetric, origin symmetric or neither.
When I plug (-x) into the equation it does not come out to be y-axis symmetric and when I multiple each side by (-1) it does not come out to be origin symmetric. So, my answer is neither.
Am I figuring this out correctly?
Lori
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
You are correct. When working with polynomials, the graph will be y-axis symmetric if EVERY exponent is an even exponent. Since there are no even exponents, it's not y-axis symmetric. On the other hand, the graph will be origin symmetric only if EVERY exponent is an odd exponent. Since has an even exponent (not odd), this rules out symmetry with respect to the origin as well. If the function was , then you'd find that the graph was symmetric to the origin (go ahead and test it if you want).
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