1 / 11

Introduction to Limits, Continuity , and End Behavior

Introduction to Limits, Continuity , and End Behavior. Honors Precalculus Functions Mr. Frank Sgroi , M.A.T. Holy Cross high School.

lucas-bonner
Download Presentation

Introduction to Limits, Continuity , and End Behavior

An Image/Link below is provided (as is) to download presentation 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. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Introduction to Limits, Continuity , and End Behavior Honors Precalculus Functions Mr. Frank Sgroi, M.A.T. Holy Cross high School

  2. 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

  3. We express this concept in symbolic notation as follows: Read: The limit of f(x) as x approaches c is L From the previous example the notation would be: Limit Notation

  4. 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

  5. A function that is NOT continuous is said to be discontinuous. A few examples are: Jump Discontinuity Infinite Discontinuity Removable Discontinuity Discontinuous Functions

  6. 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

  7. 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

  8. The following functions are NOT continuous because… The function is NOT defined at x = 2. Examples of Discontinuity

  9. 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

  10. Consider the graph of the function As x moves to the right the values of y become larger. Using limits… As x moves to the left the values of y become larger. Using limits … End Behavior (Example)

  11. Consider the graph of the function shown. The end behavior for this function is described as follows: End Behavior Example

More Related