y = x^5 + x^3 + 3
To determine whether is function is even or odd, we need to replace x with -x
let y = f(x)
therefore, f(x) = x^5 + x^3 +3
substitute -x into f
f(-x) = (-x)^5 + (-x)^3 + 3
in algebra, If a negative value is raised to an odd power, then the value become negative but if it is raised to an even power the value become positive
f(-x) = -x^5 + (-x^3) +3
minus x plus = minus
f(-x) = -x^5 - x^3 +3
therefore, this function is an odd function because the sign is opposite to the initial expression
f(x) = x^5 + x^3 + 3
f(-x) = -x^5 - x^3 +3
The two expressions remain the same but different signs and this make the function to be an odd function.