Lesson 9 Absolute Value as Distance Graphing Special Functions

Slides:

Advertisements

Similar presentations

1.4 Calculating limits. Limit Laws Suppose that c is a constant and the limits and exist. Then.

Advertisements

EXAMPLE 1 Graph a quadratic function in vertex form 14

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

The Derivative of a Logarithm. If f(x) = log a x, then Notice if a = e, then.

Log a x y. Recognize and evaluate logarithmic functions with base a Graph logarithmic functions Recognize, evaluate, and graph natural logarithmic 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.

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.

Lesson 12-2 Exponential & Logarithmic Functions

EXAMPLE 1 Graph a quadratic function in vertex form Graph y = – (x + 2) SOLUTION STEP 1 Identify the constants a = –, h = – 2, and k = 5. Because.

Graphing quadratic functions (Section 5.1. Forms of the quadratic function  Standard form  Vertex form  Intercept form.

GRAPHING REFLECTIONS OF PARABOLAS. Review: Reflections  A reflection is the result of replacing x with –x or f(x) with –f(x).  The former causes a reflection.

Lesson 9.1 Page #1, 3, 7-19 (ODD), (EOO),35, (ODD), (EOO), (EOO), 83, 85, 91.

Problem of the Day Divide:.

Example 2 Finding Absolute Value An eyeglass prescription is given as a positive or negative number. A prescription for a person who is farsighted is positive.

2-7 Absolute Value Function Objective: I can write and graph an absolute value function.

Everyone needs a small white board, marker, and eraser rag 1.

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.

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

2-2 Extension Part 2: Piecewise Functions

Lesson Identifying Opposites and Absolute Value of Rational Numbers

Unit 3 Functions and Graphs

Algebra 1 Notes: Lesson 2-1 Rational Numbers on the Number Line

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 1. On approximately what interval is the function is decreasing. Are there any zeros? If so where? Write the equation of the line through.

Homework Log Fri 10/2 Lesson 2 – 7 Learning Objective:

Absolute Value Functions

Graph Absolute Value Functions using Transformations

22 – The Absolute Value Function No Calculator

I can Shift, Reflect, and Stretch Graphs

Warm Up State the domain and range of the following equations:

Quadratic Functions, Translation and Reflection

Chapter 2: Analysis of Graphs of Functions

Graph Absolute Value Functions using Transformations

Graph Absolute Value Functions using Transformations

6.5 Solving Open Sentences involving Absolute Value

Lesson 5-1 Graphing Absolute Value Functions

3.1 Quadratic Functions and Models

4.3 Symmetry Which graph is NOT a 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.

Step functions Greatest integer functions Piecewise functions

Graphing and Evaluating The Piecewise Function A Series of Examples

2.7 Graphing Absolute Value Functions

Graphing Absolute Value Functions

Date Library of Functions

Parabolas Objective: Be able to identify the vertex, focus and directrix of a parabola and create an equation for a parabola. Thinking Skill: Explicitly.

Piecewise Functions.

3.1 Quadratic Functions and Models

(4)² 16 3(5) – 2 = 13 3(4) – (1)² 12 – ● (3) – 2 9 – 2 = 7

Absolute Value Inequalities

Piecewise-Defined Function

Inverse Functions and Relations

2.7 Graphing Absolute Value Functions

§ 8.3 Graphing Piecewise-Defined Functions and Shifting and Reflecting Graphs of Functions.

Warm-Up 4 minutes Graph each function: 1) Y = 3x - 2 Y = -½x + 4 Y = 8

Unit 3- Lesson 5.6 Absolute Value Inequalities

Graphing Quadratic Functions

I can graph a function with a table

Piecewise-defined Functions

Parabolas a set of points whose distance to a fixed point (focus) equals it’s distance to a fixed line (directrix) A Parabola is -

Warm up Solve and graph on number line 5|x+2| - 3 < 17

9.4 Absolute Value Functions and Graphs

Please get out a couple of sheets of graph paper for this lesson!!

Special Functions Constant Step Absolute Value Piece Wise Identity.

Presentation transcript:

Lesson 9 Absolute Value as Distance Graphing Special Functions Logs base 10 and natural base

Absolute Value of distance | x – a | = d What number is distance d from a? a + d a - d a

Absolute Value of distance | x – a | < d What number is distance less than d from a? a + d a - d a

Absolute Value of distance | x – a | > d What number is distance greater than d from a? a + d a - d a

Write down in notes! 3/5 + 2/5 = 1 3/5 – 2/5 =1/5 3/5

You try on white board

Special Functions Suppose you have a function f(x). Then | f(x) | has the same graph of f(x) except when f(x)<0 If f(x) < 0, then the graph is reflected over the x-axis.

Absolute Value Function

Sine Graph

Parabola

Piecewise defined function

Log properties