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

Algebra ->  Functions -> 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      Log On


   

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) About Me  (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 3=3x%5E0 has an even exponent (not odd), this rules out symmetry with respect to the origin as well. If the function was f%28x%29=x%5E1171+-+5x%5E109, then you'd find that the graph was symmetric to the origin (go ahead and test it if you want).