Introduction to Limits, Continuity , and End Behavior. Honors Precalculus Functions Mr. Frank Sgroi , M.A.T. Holy Cross high School.
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
Honors Precalculus Functions
Mr. Frank Sgroi, M.A.T.
Holy Cross high School
The limit of a function (if it exists) is a number that the y-value of a function approaches as the x-value approaches a specific number. The diagram below may be of assistance.
Notice: As x gets closer to 2 (from either direction), y gets closer to 2 (from both directions). So the limit =2.Intuitive Definition of a Limit
Read: The limit of f(x) as x approaches c is L
From the previous example the notation would be:Limit Notation
A function is said to be continuous if “you can draw the graph of a function without lifting your pencil off of the paper”. A few examples are:The Concept of Continuity
Knowing whether a function is continuous or discontinuous is very useful when analyzing the graph and properties of a function.
To completely understand the idea of a continuous function we must construct a formal definition.Continuity
A function f is continuous at x = c if and only if each of the following conditions is met:
(i) f(x) is defined at x = c.
If any of the above conditions is not met then the function is said to be discontinuous at x = c.Definition of Continuity
The function is NOT defined at x = 2.Examples of Discontinuity
One of the applications of limits is to describe the “end behavior” of a function. This idea explains how functions behave as the values of x “increase without bound” or “decrease without bound”.End Behavior of a Function