Loading in 5 sec....

Introduction to Limits, Continuity , and End BehaviorPowerPoint Presentation

Introduction to Limits, Continuity , and End Behavior

- 81 Views
- Uploaded on

Download Presentation
## PowerPoint Slideshow about ' Introduction to Limits, Continuity , and End Behavior' - lucas-bonner

**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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

### Introduction to Limits, Continuity , and End Behavior

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 LimitWe 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 NotationA 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 ContinuityA function that is NOT continuous is said to be discontinuous. A few examples are:

Jump

Discontinuity

Infinite

Discontinuity

Removable

Discontinuity

Discontinuous FunctionsKnowing 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.

ContinuityA function very useful when analyzing the graph and properties of 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 ContinuityThe following functions are NOT continuous because… very useful when analyzing the graph and properties of a function.

The function is NOT defined at x = 2.

Examples of DiscontinuityOne 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 FunctionConsider the graph of the function behavior” of a function. This idea explains how functions behave as the values of x “increase without bound” or “decrease without bound”.

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)Consider the graph of the function shown. behavior” of a function. This idea explains how functions behave as the values of x “increase without bound” or “decrease without bound”.

The end behavior for this function is described as follows:

End Behavior Example
Download Presentation

Connecting to Server..