Algebra of Continuous Functions

The video tutorial explores the concept of continuity in functions, focusing on the algebra of functions and how continuity applies to the sum, difference, product, and quotient of functions. It demonstrates that if two functions are continuous at a point, their sum, difference, product, and quotient (provided the denominator is not zero) are also continuous at that point. The tutorial further examines the continuity of rational and composite functions, using examples like sine and cosine functions to illustrate these principles.

Describe the continuity of the function sine X plus cos X.

What is the continuity of the function tan X in its domain?

What is the role of polynomial functions in determining the continuity of rational functions?

How does the composition of functions affect their continuity?