In this section we will…  Determine the continuity or discontinuity of a function.  Identify the end behavior of functions.  Determine whether a function is increasing or decreasing on an interval.

 A continuous function’s graph can be drawn without ever lifting up your pencil.  It has no holes or gaps.  All x-values are defined.

 Function is undefined at a value but, otherwise, the graph matches up.  Graph has a “hole”.

 Graph stops at one y- value, then “jumps” to a different y-value for the same x-value.  Common in piece- wise functions.

 A major disruption in the graph.  As graph approaches the domain restriction, the graph will shoot towards either positive or negative infinity.

1. Continuous or Not Continuous 2. If not continuous, Type of Discontinuity 3. Which test it failed (only need one) 4. Domain and Range

 A function is continuous on an interval iff it is continuous at each number in the interval.

 Increasing means uphill left to right.  Decreasing means downhill left to right.  Constant means a flat or horizontal line left to right.

 P 166 #26, 28, 30  Determine the intervals where the functions are increasing or decreasing.  Write the intervals in interval notation and in in terms of x.

 What will the function be doing at the outermost reaches of its domain and range?

 Given the following function, determine its continuity, behavior over its domain and end behavior.

 HW 2.3: P 166 #13 – 31 odd, 39  You will need a graphing calculator.