Given a piecewise function evaluate the limits

The video tutorial explains how to graph two functions: the negative absolute value of X and X^2 + 1. It discusses how to reflect the absolute value function and shift the quadratic function. The tutorial also covers how to handle these functions as piecewise functions, focusing on specific domains. Finally, it explores the concept of limits as X approaches zero from both the left and right, emphasizing the importance of graphing each function separately.

What happens to the graph of the absolute value function when it is multiplied by a negative number?

Describe the characteristics of the quadratic function X^2 + 1.

What does it mean to have a hole in the graph of a function?

Explain the significance of the limits as X approaches zero from the left and right.

How do you graph piecewise functions, and what should you consider?