Question

Determine if each function is even, odd or neither. Show all work and include an explanation of any symmetry that exists.

A) y = x^4 + 4x^2

B) y = 3x^3 - x - 3

C) y = x^5 - x^3 + x

D)y = 3

Answer 1

even if f(-x) = f(x)
odd if f(-x) = -f(x)

A even
B neither
C odd
D even

all even functions have axis of symmetry at y=0

all odd functions are radially symmetric about (0,0)

a product of an even and an odd function is odd.

y=3x^3 - x - 3 = 3x(x^2 - 1/3) - 3

so, since x^2-1/3 is even, and 3x is odd, 3x(x^2 - 1/3) is odd.

y is radially symmetric about (0,-3)