Lecture: 1D Pre AP & GT Precalculus

Slides:

Advertisements

Similar presentations

Lesson 1.1 Essential Ideas A relation is a set of ordered pairs mapping between two sets, the domain and range. A relation is a set of ordered pairs mapping.

Advertisements

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

1.5 I understand Functions. Function For each input there is only one output Ex: Let g represent the age of a US citizen and d represent the number of.

Name That Graph…. Parent Graphs or Base Graphs Linear Quadratic Absolute Value Square Root Cubic Exponential Math

Library of Functions.

Copyright © Cengage Learning. All rights reserved. 2 Functions and Their Graphs.

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

Chapter 2.2 Algebraic Functions. Definition of Functions.

SWBAT: −Match functions to their parent graphs −Find domain and range of functions from a graph −Determine if a function is even or odd −Give the domain.

Graphs of Functions (Part 2) 2.5 Graphing calculator day.

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.

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.

3.3 Library of Functions, Piecewise-Defined Functions

3.3-2 Step, Piecewise, Absolute Value Functions. Outside of linear and non-linear, we have a special set of functions whose properties do not fall into.

Unit 1, Part 2 Families of Functions, Function Notation, Domain & Range, Shifting.

Activity 1.6 Depreciation. In your groups… Read page 51 Complete exercises 1 and 2 in your groups Don’t forget –Average rate of change is –UNITS!!!!!!!!!!!!!!!!!!!!!!!!!

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.

Unit 1 Review Standards 1-8. Standard 1: Describe subsets of real numbers.

Notes Over 4.8 Identifying Functions A relation where each input has exactly one output. Function Decide whether the relation is a function. If it is.

2-2: Piecewise Functions Unit 2: Linear Functions English Casbarro.

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.

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.

CHAPTER 1.7 Piecewise Functions.

Review Chapter 1 Functions and Their Graphs. Lines in the Plane Section 1-1.

PARENT FUNCTIONS Constant Function Linear (Identity) Absolute Value

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

Copyright © Cengage Learning. All rights reserved. 1 Functions and Their Graphs.

Bell Ringer 1. What are the ways to solve a system of equations?

Function Notation and Parent Functions

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

Today in Pre-Calculus Turn in info sheets

Copyright © Cengage Learning. All rights reserved.

Estimate and classify the extrema for f (x)

Find the x and y intercepts.

A Library of Parent Functions

Describe subsets of real numbers.

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.

1.6 A Library of Parent Functions

PIECEWISE FUNCTIONS.

Calculus section 1.1 – 1.4 Review algebraic concepts

How can I analyze graphs of FUNctions?

4.8 Functions and Relations

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Functions and Their Graphs

Increasing, Decreasing, and Piecewise Functions; Applications

Functions, Symmetry, and the Parent Functions

Sec. 2.4 Library of Functions

I can Shift, Reflect, and Stretch Graphs

Roll of “a” Roll of “h” Roll of “k” Who’s your Daddy? Switch

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.

Parent Functions.

Step functions Greatest integer functions Piecewise functions

Functions F.IF.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly.

Parent Functions.

Determining the Key Features of Function Graphs

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Functions, Symmetry, and the Parent Functions

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

2.1 Rates of Change and Limits

Unit 1 Day 8 Inverse Functions

Horizontal shift right 2 units Vertical shift up 1 unit

Horizontal Shift left 4 units Vertical Shift down 2 units

Section 2-2 Linear Equations Objective:

Review for Test #1 Calculus – Larson.

Special Functions Constant Step Absolute Value Piece Wise Identity.

Presentation transcript:

Lecture: 1D Pre AP & GT Precalculus Parent Functions Lecture: 1D Pre AP & GT Precalculus

Function Notation When referring to the output of a function, we typically use f(x) to denote the y-value output associated with an inputted x-value. This notation is due to Leonhard Euler (pronounced: Oiler)

Constant Function

Linear Function

Review: Linear Functions

Linear Function Example Find the equation of the linear function through the points (-1,2) and (3.-4) Be Careful not to do too much algebra

Quadratic Functions

Square Root Function

Average Rate of Change

Average Rate Example What is the Average Rate of Change of the general quadratic between x=-1 and x=2

Average Rate of Change Example On the Westpark Tollway, one tollbooth is located at mile marker 52 and another is located at 62. The elapsed time between tollbooths for a driver is 7.5 minutes? What is the driver’s average speed on that interval? Hint: Distance is a function of time

Average Rate of Change Example Reflection: What does this mean? According to the mean value theorem from calculus, averaging a speed of 80 means that at one point on the interval, the driver was going 80 mph. Since the speed limit is less than 80 mph, cops can give tickets from EZ Tag Data

Piecewise Function (definition) A function whose definition is given differently on disjoint subsets of its domains. Notation: Absolute Value Example

Graph this function:

Piecewise Function Reflection: Why is the notion of disjoint domain subsets important in the definition of a piecewise function? If the function value was doubly defined for any point on the domain, it would fail the vertical line test and not be a function

Greatest Integer Function Also called a Step Function or Floor Function (notation) [[x]] (verbal definition) the function which outputs the greatest integer less than or equal to the input.

Greatest Integer Examples What is [[π]]? [[π]] = 3 What is [[-π]]? [[− π]]= − 4

Step Functions Reflection: What are some real life situations that can be modeled by a step function? Digital Signals, Power Switches