Answer: C. g(x) = x^4 - x^2 + 0.5
Why is this?
We start with x^4 - x^2, which is the original f(x) function. Adding some number to this result will increase the y coordinate of any point on the f(x) function. This is because y = f(x). The only thing that matches is choice C, where we shift the graph up 0.5 units. We say that g(x) = f(x) + 0.5
Choice D goes in the opposite direction, and shifts the graph down 0.5 units.
Choices A and B shift the graph horizontally to the right 0.5 units and to the left 0.5 units respectively.
