This video introduces some of the important continuity theorems used in calculus. We begin by talking about the algebra of continuous functions and then use the fact that x is continuous to build up that polynomials and rational functions are continuous. We then introduce a list of functions continuous on their domains:
• Polynomials
• Rational Functions
• Trigonometric Functions
• Inverse Trigonometric Functions
• Exponential Functions
• Logarithmic Functions
• Radicals
• Absolute value

We then move on to a theorem stating that the composition of continuous functions is continuous before moving on to three examples including a rational function, a half circle, and a composite function – we find the domains on which they are continuous.