Continuous & Types of Discontinuity

Slides:

Advertisements

Similar presentations

Horizontal Vertical Slant and Holes

Advertisements

9.3 Rational Functions and Their Graphs

Graphing Rational Functions

Point of Discontinuity

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,

Introduction to Rational Equations. 2 Types of Functions Continuous Discontinuous.

Introduction to Rational Equations. 2 Types of Functions Continuous Discontinuous.

Continuity 2.4.

Section Continuity. continuous pt. discontinuity at x = 0 inf. discontinuity at x = 1 pt. discontinuity at x = 3 inf. discontinuity at x = -3 continuous.

Continuity TS: Making decisions after reflection and review.

Section 1.4 Continuity and One-sided Limits. Continuity – a function, f(x), is continuous at x = c only if the following 3 conditions are met: 1. is defined.

RATIONAL FUNCTIONS A rational function is a function of the form:

Introduction to Rational Equations 15 November 2010.

Lesson 2.6 Rational Functions and Asymptotes. Graph the function: Domain: Range: Increasing/Decreasing: Line that creates a split in the graph:

Rational Functions A function of the form where p(x) and q(x) are polynomial functions and q(x) ≠ 0. Examples: (MCC9-12.F.IF.7d)

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.

2.5 – Continuity A continuous function is one that can be plotted without the plot being broken. Is the graph of f(x) a continuous function on the interval.

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

Informal Description f(x) is continuous at x=c if and only if there are no holes, jumps, skips or gaps in the graph of f(x) at c.

8-3 The Reciprocal Function Family

Removable Discontinuities & Vertical Asymptotes

8.3 Holes and Vertical Asymptotes. Points of Discontinuity (POD) : These are the values that make the factors in the denominator = 0. POD = Restricted.

9.3 – Rational Function and Their Graphs. Review: STEPS for GRAPHING HOLES ___________________________________________ EX _________________________________________.

I can graph a rational function.

Lesson 8-3: Graphing Rational Functions

Section Continuity 2.2.

C ONTINUITY AND L IMITS Review 2. Does the function exist everywhere? Continuity Informally, a function is continuous where it can be drawn without lifting.

Definition: Continuous A continuous process is one that takes place gradually, without interruption or abrupt change.

1 Limits and Continuity. 2 Intro to Continuity As we have seen some graphs have holes in them, some have breaks and some have other irregularities. We.

GRAPHS OF RATIONAL FUNCTIONS F-BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of.

Asymptotes of Rational Functions 1/21/2016. Vocab Continuous graph – a graph that has no breaks, jumps, or holes Discontinuous graph – a graph that contains.

V ERTICAL AND H ORIZONTAL A SYMPTOTES. V ERTICAL A SYMPTOTES To find Vertical Asymptotes: Step1. Factor the top and bottom of the function completely.

Lesson 21 Finding holes and asymptotes Lesson 21 February 21, 2013.

Warm UpMar. 12 th  Solve each rational equation or inequality.

CHAPTER 9: RATIONAL FUNCTIONS. 9.1 INVERSE VARIATION.

Bell Ringer  1. In a rational function, what restricts the domain (hint: see the 1 st Commandment of Math).  2. What are asymptotes?  3. When dealing.

9.3 – Rational Function and Their Graphs

2.5 Exploring Graphs of Rational Functions

Rational Functions Algebra

Ch. 2 – Limits and Continuity

Horizontal Vertical Slant and Holes

Unit 4: Graphing Rational Equations

Limits, Asymptotes, and Continuity

Ch. 2 – Limits and Continuity

Section 5.4 Limits, Continuity, and Rational Functions

5-Minute Check Lesson 3-5 Find the inverse of y = - 3x + 4 Then graph both on the same coordinate axes. What is the relationship between a graph of a.

Piecewise Functions.

2.5 Piecewise Functions.

2.5 Piecewise Functions.

Objectives: 1. Graph Piecewise Functions 2

Section 2.2 Objective: To understand the meaning of continuous functions. Determine whether a function is continuous or discontinuous. To identify the.

Introduction to Rational Equations

Piecewise Functions.

Piecewise Functions.

26 – Limits and Continuity II – Day 1 No Calculator

Horizontal Vertical Slant and Holes

Rational Functions Section 8.3 Day 2.

Functions and Graphs Chapter 1, Section 2.

Graphing rational functions

EQ: What other functions can be made from

Which is not an asymptote of the function

December 15 No starter today.

Continuity of Function at a Number

Horizontal Vertical Slant and Holes

Section 5.4 Limits, Continuity, and Rational Functions

5-Minute Check Lesson 3-5 Find the inverse of y = - 3x + 4 Then graph both on the same coordinate axes. What is the relationship between a graph of a.

Presentation transcript:

Continuous & Types of Discontinuity Math 3 Unit 7 Continuous & Types of Discontinuity

Compare and Contrast

What is the difference between the graphs in the first group and the second?

Continuous A Function is CONTINUOUS if there are no holes, breaks or jumps. This graph is “unbroken”

Discontinuity Discontinuities are x-values that create holes, jumps, asymptotes or breaks in graphs. TYPES: Holes (also known as removable) Jumps Asymptotes

Identify Discontinuity

Identify Discontinuity

Identify Discontinuity

Identify Discontinuity

Identify Discontinuity

Reasons for Discontinuity Zero in the bottom of a fraction (Remember holes are what crosses out, and Vertical Asymptotes are what are left in the bottom!) Pieces in a Piecewise function not matching

Type 1

Type 1

Type 2

Type 2

Type 2