Continuity and End Behavior

Slides:

Advertisements

Similar presentations

3.5 Continuity & End Behavior

Advertisements

Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

1.2 Functions & their properties

Identifying Quadratic Functions

Exponential Functions

Rational Functions.

Warm-up 1. Given this relation:

Section 8.3 Absolute Value Functions. 8.3 Lecture Guide: Absolute Value Functions Objective 1: Sketch the graph of an absolute value function.

4.22 Domain and Range from a Graph Nov. 10 and 11.

In this section we will…  Determine the continuity or discontinuity of a function.  Identify the end behavior of functions.  Determine whether a.

Objectives: 1.Be able to define continuity by determining if a graph is continuous. 2.Be able to identify and find the different types of discontinuities.

 Lesson 1: 2.1 Symmetry (3-1)  Lesson 2: 2.2 Graph Families (3-2, 3-3) Lesson 2:  Lesson 3: 2.3 Inverses (3-4) Lesson 3:  Lesson 4: 2.4 Continuity.

Continuity When Will It End. For functions that are "normal" enough, we know immediately whether or not they are continuous at a given point. Nevertheless,

Chapter 3: The Nature of Graphs Section 3-1: Symmetry Point Symmetry: Two distinct points P and P’ are symmetric with respect to point M if M is the midpoint.

 A continuous function has no breaks, holes, or gaps  You can trace a continuous function without lifting your pencil.

Continuity Section 2.3.

Pre Calculus Functions and Graphs. Functions A function is a relation where each element of the domain is paired with exactly one element of the range.

Today in Pre-Calculus Review Chapter 1 Go over quiz Make ups due by: Friday, May 22.

X-intercept(s): y-intercept: Domain: Axis of Symmetry: Zero(s): Range: What are the Characteristics of Quadratic Functions?? MM2A3c. Investigate and explain.

Holt Algebra Identifying Quadratic Functions 9-1 Identifying Quadratic Functions Holt Algebra 1 Warm Up Warm Up Lesson Presentation Lesson Presentation.

Check it out! : Comparing Linear Functions.

Math II Unit 5 (Part 1). Solve absolute value equations and inequalities analytically, graphically and by using appropriate technology.

Quadratic Vocabulary Words to graph by….

Continuity (Section 2.6). When all of the answers are YES, i.e., we say f is continuous at a. Continuity limit matches function value 1.Is the function.

Objectives: 1.Be able to define continuity by determining if a graph is continuous. 2.Be able to identify and find the different types of discontinuities.

Copyright © Cengage Learning. All rights reserved. 4 Quadratic Functions.

A function, f, is continuous at a number, a, if 1) f(a) is defined 2) exists 3)

Curve Sketching with Radical Functions

Section 7.2: Linear and Absolute Value Functions.

Domain and Range of Quadratic Functions

Section 8.5 Analyzing Graphs. 8.5 Lecture Guide: Analyzing Graphs Objective 1: Identify a function as an increasing or decreasing function.

CPM Section 7.1 “The Rational Function”. In Chapter 4, we discussed the linear function. In Ch. 5, it was the absolute value function and in Chapter 6.

Domain/Range Continuous/Discontinuous Increasing/Decreasing Constant.

Date: 1.2 Functions And Their Properties A relation is any set of ordered pairs. The set of all first components of the ordered pairs is called the domain.

2.4 Continuity Objective: Given a graph or equation, examine the continuity of a function, including left-side and right-side continuity. Then use laws.

Warm up  Graph the function and its inverse:  Find for the relation. Then state whether is a function.

1.3 Limits, Continuity, & End Behavior September 21 st, 2015 SWBAT estimate a limit of a graphed function. SWBAT identity a point of discontinuity utilizing.

Domain and Range: Graph Domain- Look horizontally: What x-values are contained in the graph? That’s your domain! Range- Look vertically: What y-values.

3-5 Continuity and End Behavior Pre Calc A. Discontinuous vs Continuous.

Analyzing and sketching the graph of a rational function Rational Functions.

1 The graph represents a function because each domain value (x-value) is paired with exactly one range value (y-value). Notice that the graph is a straight.

Functions and Their Properties Section 1.2 Day 1.

Symmetry and Coordinate Graphs Section 3.1. Symmetry with Respect to the Origin Symmetric with the origin if and only if the following statement is true:

Today in Pre-Calculus Do not need a calculator Review Chapter 1 Go over quiz Make ups due before: Friday, May 27.

 1. Given this relation:  {(2, -1), (4, -1), (3, 2), (5, 1), (4, 2), (5, 1)}  Domain?  Range?  Function or Not? Explain why?  2. Convert these to.

Objectives Identify quadratic functions and determine whether they have a minimum or maximum. Graph a quadratic function and give its domain and range.

SECONDARY MATH 3 4-2COMPARING FUNCTIONS AND DOMAIN.

Decide whether each of the following is continuous or not.

Functions and Their Properties

Warm-Up: Use the graph of f (x) to find the domain and range of the function.

25. Rational Functions Analyzing and sketching the graph of a rational function.

Function Characteristics - Domain and Range

1.5 The Limit of a Function.

3-6 Critical Points and Extrema

Use the graph of f (x) to find the domain and range of the function.

Continuity, End Behavior, and Limits Unit 1 Lesson 3

4.5 An Algorithm for Curve Sketching

A. 4 positive zeros; 1 negative zero

Domain and Range.

3-5 Continuity and End Behavior

Precalculus PreAP/Dual, Revised ©2018

Section 5 – Continuity and End Behavior

Continuity A function is Continuous if it can be drawn without lifting the pencil, or writing utensil, from the paper. A continuous function has no breaks,

Warm up Write the equation in vertex form of the quadratic equation that has been: 1. shifted right 7 and down reflected across the x-axis and shifted.

55. Graphing Exponential Functions

4.2 Critical Points, Local Maxima and Local Minima

Presentation transcript:

Continuity and End Behavior Section 3-5

I can determine whether a function is continuous or discontinuous Learning Target I can determine whether a function is continuous or discontinuous I can identify the end behavior of functions I can determine whether a function is increasing or decreasing on an interval

The chart below shows the different types of discontinuous functions. Continuous Function-the graph of this function is smooth or continuous curves. (Linear and Quadratic Function) Discontinuous function- the graph of this function cannot be trace without lifting your pencil (step wise and absolute value). The chart below shows the different types of discontinuous functions. Function Name Graph Characteristics Infinite Discontinuity The graph becomes greater and greater as it approaches a given x-value.

Jump Discontinuity Point Function Name Graph Characteristics Jump Discontinuity The graph stops at a given value of the domain and then begins again at a different range value for the same value of the domain. Point When there is a value in the domain for which the function is undefined, but the pieces of the graph match up. There is a hole in the graph.

Continuity Test A function is continuous at x = c if it satisfies the following conditions: 1. the function is defined at c; or f(c) exists 2. the function approaches the same y-value on the left and right sides of x = c 3. the y-value that the function approaches from each side is f(c).

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

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.

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=