HPC 2.4 – Library of Functions; Piecewise-Defined Functions

Slides:

Advertisements

Similar presentations

A Library of Functions This presentation will review the behavior of the most common functions including their graphs and their domains and ranges. See.

Advertisements

1 © 2010 Pearson Education, Inc. All rights reserved © 2010 Pearson Education, Inc. All rights reserved Chapter 2 Graphs and Functions.

Properties of Functions

Day 5 Book Section 7.8 Get 2 grids for the 2 shift problems!

Properties of Functions Section 1.6. Even functions f(-x) = f(x) Graph is symmetric with respect to the y-axis.

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

Library of Functions; Piecewise-defined Functions February 5, 2007.

Chapter 2 Functions and Graphs Section 2 Elementary Functions: Graphs and Transformations.

Library of Functions.

A Library of Parent Functions Digital Lesson. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 Definition: Functions Linear Function.

Library of Functions You should be familiar with the shapes of these basic functions. We'll learn them in this section.

Graphing Piecewise Functions

2.2 Function Library Learning Objective: to identify different types of functions and their transformations. Also, to graph piecewise functions. Warm-up.

Functions and Graphs 1.2. FUNCTIONSFUNCTIONS Symmetric about the y axis Symmetric about the origin.

Properties of Functions Operations on Functions

1.3 Families of Equations. What families of graphs have your studied? Linear Absolute Value Quadratic Square Root Cubic Cube Root.

Chapter 2 Functions and Graphs Section 2 Elementary Functions: Graphs and Transformations.

A Library of Parent Functions Objective: To identify the graphs of several parent functions.

Library of Functions You should be familiar with the shapes of these basic functions. We'll learn them in this section.

2.3 Introduction to Functions

3.3 Library of Functions, Piecewise- Defined Functions.

Section 1.3 – More on Functions. On the interval [-10, -5]: The maximum value is 9. The minimum value is – and –6 are zeroes of the function.

The Twelve Basic Functions

Honors Pre-Calculus Library of Functions, Piecewise- Defined Functions.

3.3 Library of Functions, Piecewise-Defined Functions

Section 3.4 Library of Functions; Piecewise-defined Functions.

R Functions in one variable can be represented by a graph. R Each ordered pair (x, f(x)) that makes the equation true is a point on the graph. R Graph.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 3.4 Library of Functions; Piecewise-defined Functions.

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,

basic functions.

Objectives: Graph the functions listed in the Library of Functions

Library of Functions You should be familiar with the shapes of these basic functions. We'll learn them in this section.

Continuity (Informal Definition)

Hot Seat Game!!! Review of Basic Graphs. Which 3 functions DO NOT have all Real #’s as their domain?

A Library of Parent Functions. The Constant Parent Function Equation: f(x) = c Domain: (-∞,∞) Range: [c] Increasing: None Decreasing: None Constant: (-∞,∞)

Chapter 2 Functions and Graphs Section 2 Elementary Functions: Graphs and Transformations.

1.6 A Library of Parent Functions Ex. 1 Write a linear function for which f(1) = 3 and f(4) = 0 First, find the slope. Next, use the point-slope form of.

Graphing Cubed Roots Without a Calculator Objective: You should be able to graph cubed root functions (including their changes) without a calculator.

Trig/Pre-Calculus Opening Activity

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.

1 Copyright © 2015, 2011, and 2008 Pearson Education, Inc. Chapter 1 Functions and Graphs Section 2 Elementary Functions: Graphs and Transformations.

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

1.6 A Library of Parent Functions

1.6 A Library of Parent Functions Ex. 1 Write a linear function for which f(1) = 3 and f(4) = 0 First, find the slope. Next, use the point-slope form of.

Section 3.4 Library of Functions; Piecewise-Defined Functions.

HPC 2.1 – Functions Learning Targets: -Determine whether a relation represents a function. -Find the value of a function. -Find the domain of a function.

PARENT FUNCTIONS Constant Function Linear (Identity) Absolute Value

Parent Functions. Learning Goal I will be able to recognize parent functions, graphs, and their characteristics.

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

Copyright © 2015, 2011, 2005 Pearson Education, Inc.

Chapter 2 Functions and Graphs

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.

PIECEWISE FUNCTIONS.

2.4 Library of Functions, Piecewise-Defined Functions

2.4 Library of Functions, Piecewise-Defined Functions

Sec. 2.4 Library of Functions

Domain, Range, Maximum and Minimum

1.6 A Library of Parent Functions

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.

Piecewise-defined Functions

Go Over HW Answers: Domain & Range HW WKS

Parent Functions.

Parent Functions.

Date Library of Functions

Topic/ Objective: To evaluate and graph piecewise and step functions.

2.4 Library of Functions, Piecewise-Defined Functions

Unit 4: Transformations and piecewise functions

Presentation transcript:

HPC 2.4 – Library of Functions; Piecewise-Defined Functions Learning Targets: -Graph the “library of functions” -Graph piecewise-defined functions

Please use your books to fill in the “Library of Functions” sheet.

Linear Function Domain: Range:

Constant Function Domain: *Range:

Identity Function Domain: Range:

Square Function Domain: *Range:

Cube Function Domain: Range:

Square Root Function *Domain: *Range:

Reciprocal Function *Domain: *Range:

Absolute Value Function Domain: *Range:

Greatest-Integer Function Domain: *Range:

Piecewise-Defined Functions When functions are defined by more than one equation. Certain pieces (equations) are valid for certain x’s. Each piece (equation) can be any of the functions from the library of functions.

Ex 1) a) f(-1) = b) f(1) = c) f(3) = Domain = Sketch the graph

Ex 2) An economy car rented in Florida from Ex 2) An economy car rented in Florida from Good Car Rental on a weekly basis costs $91 per week. Extra days cost $23/day until the day rate exceeds the weekly rate, in which case the weekly rate applies. Find the cost C of renting an economy car as a piecewise function of the number x of days used, where 7≤ x ≤14. * Any part of a day counts as a full day.

Ex 3) The graph of a piecewise-defined function is given Ex 3) The graph of a piecewise-defined function is given. Write a definition for the graph.