Even/Odd Function Help?

Question

Which of the following functions is neither even nor odd? Explain why.

a) f(x) = x^5

b) f(x) = tanx

c) f(x) = x^2 + 2

d) f(x) = (x-3)^2

e) f(x) = sinx

Any help on this would be appreciated. Please explain completely so that I fully understand and can do similar problems on my own. I used to know how to do this but need a refresher.Thanks so much and 10 points to a best answer.

Answer 1

A function is EVEN if f(x) = f(-x); that is, if you replace x with -x, the result of the function is the same as the original result..  

c) is an example of an even function.  We can look at one case to illustrate: if x = 2, the function evaluates to 6, and if x = -2, the expression still evaluates to 6.

A function is ODD if f(-x) = -f(x); that is, if you replace x with -x, the result of the function is the negative of the original result.

a) is an example of an odd function.  If x = 3, for example, the function evaluates to 243, but if x = -3, the function evaluates to -243.

The only one of these functions which fits neither of these criteria is d).  Again, with a test case: if x = 1, the function evaluates to 4, but if x = -1, the function evaluates to 16.  So d) is neither even nor odd.