How to find the values k that make a piecewise function continuous

The video tutorial explains how to determine the value of K that makes a function continuous. It begins by discussing the concept of continuity and discontinuity in functions, using sine of X and linear functions as examples. The tutorial then demonstrates how to evaluate the left and right hand limits at a specific point, π, to ensure continuity. Finally, it shows how to solve for K by setting the left and right hand limits equal, concluding that K must be -2π for the function to be continuous.

What is the main goal when finding the value of K in the context of function continuity?

Explain why sine of X is considered continuous for all X.

What is the significance of evaluating the left and right hand limits at π?

How do you set up the equation to find K for the function to be continuous?

What value of K makes the function continuous, and how is it derived?