Continuity and End Behavior

1. Continuity and End Behavior Section 3-5

2. Before finishing this section you should be able to: • Determine whether a function is continuous or discontinuous • Identify the end behavior of functions • Determine whether a function is increasing or decreasing on an interval Remember: Your textbook is your friend! This presentation is just a supplement to the text. BEFORE you view this, make sure you read this section in your textbook and look at all the great examples that are also worked there for you.

3. Most of the graphs that we have studied thus far have been smooth, continuous curves. However, some functions are known as discontinuous functions. You cannot trace the graph of the function without lifting your pencil. The chart below shows the different types of discontinuous functions.

5. If a function is not discontinuous, it is said to be continuous. Linear and quadratic functions are continuous at all points. A function is continuous at x = c if it satisfies the following conditions: the function is defined at c: in other words, f(c) exists the function approaches the same y-value on the left and right sides of x = c the y-value that the function approaches from each side is f(c).

6. Example: Determine whether the function is continuous at the given x-value.

12. Another characteristic of functions used for analysis is the monotonicity of the function. This means that on an interval, the function is increasing or decreasing on that particular interval. Whether a graph is increasing or decreasing is always judged by viewing a graph from left to right.

18. Helpful Websites Discontinuity: http://www.sparknotes.com/math/precalc/continuityandlimits/problems3.rhtml http://math.usask.ca/~maclean/101/Limits/Printables/BW/Continuity.pdf End behavior: http://www.purplemath.com/modules/polyends.htm 3-5 Self Check Quiz: http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-07-860861-9&chapter=3&lesson=5&quizType=1&headerFile=4&state=