How do you determine if ##f(x)= x^3 + 1## is an even or odd function?

neither
To determine if a function is even/odd consider the following.
• If f(x) = f( -x) , then f(x) is even
Even functions have about the y-axis.
• If f( -x) = – f(x) , then f(x) is odd
Odd functions have symmetry about the origin.
Test for even
##f(-x)=(-x)^3+1=-x^3+1 ≠f(x)##
Since f(x) ≠ f( -x) , then f(x) is not even.
Test for odd
##-f(x)=-(x^3+1)=-x^3-1≠f(-x)##
Since f( -x) ≠ – f(x) , then f(x) is not odd.
##rArrx^3+1″ is neither even nor odd”##
graph{x^3+1 [-10, 10, -5, 5]}