1. 2.4 Continuity Objective: Given a graph or equation, examine the continuity of a function, including left-side and right-side continuity. Then use laws of continuity to evaluate a limit. A function is continuous if you can draw it in one motion without picking up your pencil.

2. Determine whether the function is continuous at each of the following locations. Explain. 1.x = 0 2.x = 1 3.x = 2 4.x= 4 5.Over what interval(s) is f continuous?

3. Three types of Discontinuity – removable, jump, non-removable A. Removable Discontinuity (hole) B. Jump Discontinuity (left and right limits are not equal) (You can fill the hole by redefining the function at one point)

4. C.Non-removable “Infinite” Discontinuity (asymptote) Three types of Discontinuity – removable, jump, non-removable – the limit is infinite as c approaches c on one or both sides

5. Section 2.4, Figure 14 Page 69 Left-Continuous and Right Continuous – what does it mean?

9. Laws of Continuity – page 64

11. The Laws of Continuity are intended to help us determine the continuity of functions containing sums, products, quotients, multiples, powers, and roots without looking at a graph. Knowing that a function is continuous allows us to use direct substitution to evaluate a limit.