How to determine the global max and min from a piecewise function

The video tutorial explains how to graph the function X^2 + 1, highlighting that there are no restrictions on the interval except that X cannot equal 0. The graph is shifted up by one unit and features an open circle, indicating that the graph never actually reaches the value of 1. The tutorial discusses the absence of a minimum value due to the open circle and the lack of a maximum value as the graph continues to rise indefinitely.

How does the graph of X^2 + 1 behave to the left and right of the point where X equals 0?

What can be said about the maximum value of the function X^2 + 1?