Final answer:
The function g(x) that reflects f(x)=x^2-2 shifted up by 3 units is g(x)=x^2+1.
Step-by-step explanation:
The function g(x) that represents the graph of f(x)=x^2-2 shifted up by 3 units is g(x)=x^2 + 1.
To achieve this, we add 3 to the original function f(x), which gives us g(x) = f(x) + 3 = x^2 - 2 + 3.
Simplifying this, we get g(x) = x^2 + 1. This process of shifting a function up or down is a basic transformation in algebra, where adding a positive constant to a function results in a vertical shift upwards by the magnitude of that constant.