October 14, 2011 At the end of today, you will be able to Identify and graph step, constant, identity functions, piecewise functions, and absolute value.

Slides:

Advertisements

Similar presentations

Algebra II Piecewise Functions Edited by Mrs. Harlow.

Advertisements

Calculus Lesson 1.1 Part 3 of 3. Sketch the graph of the absolute value function:

2.5 Piecewise- defined Functions

Functions Basic Concepts Value (Image), Domain, Range, Graph.

Functions and Their Graphs. 2 Identify and graph linear and squaring functions. Recognize EVEN and ODD functions Identify and graph cubic, square root,

Families of Functions, Piecewise, and Transformations.

TH EDITION LIAL HORNSBY SCHNEIDER COLLEGE ALGEBRA.

What are piecewise functions? A __________ function consists of different function rules for different parts of the domain. 1. Graph f(x) = x

Graphing Piecewise Functions

1.3 Twelve Basic Functions

1 What you will learn today 1. How to evaluate piecewise functions 2. How to graph piecewise functions 3. How to determine piecewise functions from a graph.

FIRE UP! With your neighbor, simplify the following expression and be ready to share out ! Ready GO! (x + 3) 2 WEDNESDAY.

2.6 – Special Functions Math 2 Honors - Santowski.

2.6 Special Functions Step functions Greatest integer functions Piecewise functions.

Piecewise Graphs A piecewise function is defined by at least two equations, each of which applies to a different part of the function’s domain. One example.

Section 1.7 Piecewise Functions. Vocabulary Absolute Value Function – a piecewise function, written as f(x)=, where f(x) 0 for all values of x. Greatest.

October 3, 2012 Parent Functions Warm-up: How do you write a linear function, f for which f(1) = 3 and f(4) = 0? *Hint: y = mx + b HW 1.6: Pg. 71 #1-5,

Section 3.5 Piecewise Functions Day 2 Standard: MM2A1 ab Essential Question: How do I graph piecewise functions and given a graph, can I write the rule?

Piecewise Functions Lesson Talking Points Included

Continuity (Informal Definition)

SECTION 2.2 Absolute Value Functions. A BSOLUTE V ALUE There are a few ways to describe what is meant by the absolute value |x| of a real number x You.

Special Functions Lesson 9-7 Splash Screen LEARNING GOAL Understand how to identify and graph step functions, absolute value functions and piecewise-defined.

4 minutes Warm-Up Graph the function , and then use the horizontal-line test to determine if the inverse is a function.

1.5 – library of functions Goal: to recognize basic shapes/properties of graphs of different types of functions.

Notes Over 8.2 Recognizing Exponential Growth and Decay Exponential Growth Model Exponential Decay Model.

Domain & Range Domain & Range Algebra 1 By: A. C. Rivera.

Increasing & Decreasing Functions A function f is increasing on an interval if, for any x 1 and x 2, in the interval, x 1 < x 2 implies f(x 1 ) < f(x 2.

Piecewise Functions 2.7 What is a piecewise function? How are they evaluated, graphed, written, and used? What is a step function? What is a greatest integer.

1.6 Step and Piecewise Functions. Objective To identify and graph step and piecewise- defined functions.

Lesson 4.7 Topic/ Objective: To evaluate and graph piecewise and step functions. EQ: How can you describe a function represented by more than one equation.

Sullivan PreCalculus Section 2.4 Library of Functions; Piecewise-Defined Functions Objectives Graph the Functions in the Library of Functions Graph Piecewise-defined.

1.5 Library of Functions Classify functions and their graphs.

2.2 day 3 The Piecewise Function

Bellwork: Match the following graphs with their equations. NO CALCS! y=-x 2 X=# x=y 2 x = -y

2-6 Special Functions Objectives Students will be able to: 1) identify and graph step, constant, and identity functions 2) Identify and graph absolute.

1.6 A Library of Parent Functions

The Twelve Basic Functions Section 1.3 Pgs 102 – 103 are very important!

Section 3.5C: Graphs of Functions Sketch Piecewise-Defined Functions:

College Algebra K/DC Monday, 25 January 2016 OBJECTIVE TSW graph basic functions. TODAY’S ASSIGNMENT –Sec. 2.6: pp (1-10 all, all) –WS Greatest.

CHAPTER 1.7 Piecewise Functions.

CHAPTER 2 LESSON 6 Special Functions Vocabulary Step Function- A function whose graph is a series of line segments Greatest Integer Function- A step.

Comparing and Ordering Integers LESSON 6-2 Compare –12 and –10. Since –12 is to the left of –10, –12 < –10. Graph –12 and –10 on the same number line.

PARENT FUNCTIONS Constant Function Linear (Identity) Absolute Value

1.7 Piecewise Functions Objective: Identify and graph piecewise functions including greatest integer, step, and absolute value functions.

Algebra II Unit 1.

Objectives Vocabulary Write and graph piecewise functions.

2.6: Special Functions Algebra 2.

Warm Up Graph f(x) = 2x + 3 Graph f(x) = -3x + 1

Piecewise Functions At least 2 equations, each of which applies to a different part of the functions domain. It is like having 3 equations for 3 different.

LESSON 2–6 Special Functions.

piecewise-defined function

1-1 RELATIONS & FUNCTIONS

Objective 1A f(x) = 2x + 3 What is the Range of the function

Piecewise Functions At least 2 equations, each of which applies to a different part of the functions domain. It is like having 3 equations for 3 different.

Warm-up: Determine which of the following are functions. A. B.

Warmup: Take out homework..

Step functions Greatest integer functions Piecewise functions

Graphing and Evaluating The Piecewise Function A Series of Examples

Absolute Value and Step Functions (2.4.2)

Piecewise-Defined Function

All About Functions Chapter 2, Sections 1 & 6.

Unit 3 Functions.

Warm-up 5/22/2019 Day 6.

2.7 Piecewise Functions Algebra 2.

Graphing Quadratic Functions

2-6: Special Functions Direct Variation: A linear function in the form y = kx, where k 0 Constant: A linear function in the form y = b Identity:

Review for Test #1 Calculus – Larson.

Special Functions Constant Step Absolute Value Piece Wise Identity.

Presentation transcript:

October 14, 2011 At the end of today, you will be able to Identify and graph step, constant, identity functions, piecewise functions, and absolute value functions. Do Now: What is the domain and range of a function?

Lesson 2.6 Special Functions Five functions you need to recognize: IdentityStep Piecewise Constant Absolute Value

Step Functions The Greatest Integer, f(x) = [[x]] “What is the greatest integer less than…?” Example 1) Evaluate a) [[-1]] b)c) d) [[1.5]] Example 2) Find h(4.2), if h(x) = [[x + 3]] h(4.2) = [[ ]] h(4.2) = [[7.2]] h(4.2) = = -1 = 0 = 1

What do step functions look like? f(x) = [[x]] Make a table and find the points on a graph. Find the Domain and Range. xy Do #4 on Pg. 89 WS Domain: All reals (-∞,∞) Range: All reals (-∞,∞) 0 0 1

Graphing Piecewise-Defined Functions Sketch the graph of and find the domain and range. Make 2 tables for both cases: x ≤ 1f(x) = x + 3 x > 1f(x) = x OPEN CIRCLE! Do #9 on WS

Finish the other graphs we have not done on the WS for classwork credit!