C ONTINUITY AND L IMITS Review 2

Does the function exist everywhere? Continuity Informally, a function is continuous where it can be drawn without lifting a pencil. Roughly, continuous means “connected.” Formally, a function is continuous where its limit and function value are the same. In this course, we will work with three types of discontinuities: holes, vertical asymptotes, and jumps (breaks).

A fourth type of discontinuity is an oscillating discontinuity (these rarely appear). 1.) To investigate this fourth type, graph on a calculator and look at windows close to x = 0

Continuous?

Limits Informally, a limit is a y-value which a function approaches as x approaches some value. means as x approaches c, approaches the y-value of L.

2) Is the following continuous for all values of x? a) b) c)

3) Is the following continuous at x = 2?

Three conditions for a piecewise function to be continuous

4) Is the following continuous at x = 0?

5) Find the constant a such that the function is Continuous for the set of real numbers.

6) Find all values of a and b for which the function is continuous.

H OME W ORK Worksheet R-2