Determine algebraically whether the function f(x)=2x^42x^2 2x+1 is odd, even or neither.

Answer 1

Even: Algebraically, we substitute x as -x and if it goes back to original function, then it's even. Thus, f(-x) = f(x).
Visually, if this function is graphed and you see that it is symmetric to y-axis, then it's even.

Odd: If f(-x) = -f(x).

I will assume the function you wrote is
f(x) = 2x^4 + 2x^2 + 2x + 1

Let x be -x.
f(x) = 2(-x)^4 + 2(-x)^2 + 2(-x) + 1
f(x) = 2x^4 + 2x^2 - 2x + 1

The resulting function is neither odd or even, since it didn't result in f(x) or -f(x).