For these functions, determine which ones are EVEN. (y axis symmetry)  a) f(x)=3x^4 + 4 b) f(x) = x^3 + 4 c) f(x) = x^2 + x - 3 d) f(x) = 2x^4 + x^2 + 1 e) f(x) = 4 f) f(x) = x^4 + x^3 + x^2 + x + 1

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ishpiro eNotes educator| Certified Educator

Functions a, d, and e are even because they contain only even powers of x (or no x at all, as in e).

By definition, even function obeys the condition

f(-x) = f(x).

For any even power n of x

`(-x)^n = x^n`

So the functions that contain only even powers of x are even.