We are given function f(x) = x^4 - x^2.
We need to find the equation of function g(x) according to shown graph.
We can apply rules of transformation to get the function g(x) by using given graph.
Function g(x) graph is being shift a half or 0.5 units up of the graph f(x).
When graph shift k units up, we add k to given function.
Where k is some constant.
In the graph f(x) is being shifted 0.5 units up.
So, we would add 0.5 in f(x) = x^4 - x^2 function.
On adding 0.5 we get
g(x) = f(x)+0.5 = = x^4 - x^2 +0.5.
Therefore, correct option is second option.
g(x) = x^4 - x^2 +0.5.
