'Absolute value function' diaporamas de présentation

ALGEBRA DOMAIN (approximately 36% of test) Which function is shown on the graph? a. y = x 2 b . y = x 3 c

ALGEBRA DOMAIN (approximately 36% of test) Which function is shown on the graph? a. y = x 2 b . y = x 3 c. y = | x | d. y = 1/x 2. Sam observes that the data he collected falls in a V-shaped pattern when he graphs it. What type of function would

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Choose a category. You will be given the answer. You must give the correct question.

Jeopardy. Choose a category. You will be given the answer. You must give the correct question. Click to begin. Name the Function. Quadratic Formula. Which form?. Imaginary Numbers. Factoring. Parabolas. $100. $100. $100. $100. $100. $100. $200. $200. $200. $200.

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MAC 1105

MAC 1105. Module 5 Transformation of Graphs. Learning Objectives. Upon completing this module, you should be able to: Recognize the characteristics common to families of functions. Evaluate and graph piecewise-defined functions. Identify vertical and horizontal asymptotes.

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Chapter 2

Chapter 2. Functions and Graphs. Functions.

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Objectives

Objectives. Vertical Shifts Up and Down Horizontal Shifts to the Right and Left Reflections of Graphs Stretching and Shrinking of Graphs. Laws for Graphing Shifts. All graphs must be placed on graphing paper. We do not use ruled paper for graphing.

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Functions

Functions. Alice. Built-in Functions. We have been using built-in functions. How a function works. A function receives value(s), performs some computation on the value(s), and returns (sends back) a value. Types of Functions.

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259 Lecture 4 Spring 2010

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Pre-Calculus

Pre-Calculus . Chapter 1 Functions and Their Graphs. x. x. Warm Up 1.4. A Norman window has the shape of a square with a semicircle mounted on it. Find the width of the window if the total area of the square and the semicircle is to be 200 ft 2 . 1.4 Transformation of Functions.

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Function Families

Function Families. Lesson 1-5. Warm-up. F(x) = 3x + 3 G(x) = x/3 - 1 F(6) G(21) F(-4) G(-9) F(0) G(3) Did you notice any relationship between the F functions and the G functions?. Warm-up. Without looking back at your notes, define domain and range in your own words.

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Turn homework into the box-staple together and make sure both names are on sheet!! Sckett

Turn homework into the box-staple together and make sure both names are on sheet!! Sckett. Transformation of Functions. Linear Function f(x) = x. The squaring function . The absolute value function . Absolute value- distance from zero for order of operations works like ( ).

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Taylor Series

Taylor Series. The Coefficients of a Power Series. Coefficients of a Power Series. Suppose that we have function f given by a power series. What can we say about the relationship between f and the coefficients a 0 , a 1 , a 2 , a 3 , a 4 , a 5 , . . ?.

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5.2 Definite Integrals

5.2 Definite Integrals. Greg Kelly, Hanford High School, Richland, Washington. When we find the area under a curve by adding rectangles, the answer is called a Rieman sum . The width of a rectangle is called a subinterval . The entire interval is called the partition . subinterval.

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Differentiability, Local Linearity

Differentiability, Local Linearity. Section 3.2a. How f ( a ) Might Fail to Exist. A function will not have a derivative at a point P ( a , f ( a )) where the slopes of the secant lines,. f ail to approach a limit as x approaches a . Four instances w here this occurs:.

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Chapter 3

Chapter 3. Transformations of Graphs and Data. Transformation: 1 to 1 correspondence between sets of points (augmenting a figure) Translation: slide Scale change: shrinking or stretching a figure Translations and scale changes are two types of transformations (there are others).

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Section 2.6 Graphs of Functions

Section 2.6 Graphs of Functions. Finding function values graphically Finding Domain and Range graphically Graphs of non-linear functions Translations of graphs Reflections of graphs. Finding Function Values from a Graph. Find f(-3) Find the x value that causes f(x) = -2.

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Continuity

Continuity. What is continuity? Algebraic properties Compositions. Definition. A function f is continuous at x=c if f(c) is defined lim x ?c f(x) exits lim x ?c f(x) = f(c) If one of these fails to hold, say that f is discontinuous at c. Examples.

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Absolute Value Equations and Inequalities

Absolute Value Equations and Inequalities. Lesson 2.5. Absolute Value Function. Whatever you put into the function comes out positive. -3. +7. +7. +3. Absolute Value Function. Definition. Use the abs( ) function on your calculator. Absolute Value Function.

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Algebra II

Algebra II. Chapter 2 Linear Equations and Functions. Section 2.1 Functions and their Graphs. Definitions Relation Function Domain Range Representing Relations and Functions Mapping diagram Ordered Pairs Points on the coordinate plane Equations

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Math 170 Functions, Data, and Models

Math 170 Functions, Data, and Models. 09 Piecewise-Defined Functions Section 2.3. Comments on Lab 02. Basic Concept. A function can be defined piecewise. Tax Example. The U.S. Income Tax rates for the first three tax brackets are 10 % on taxable income from $0 to $ 8,700,

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Special functions

Special functions. Absolute Value Function. Absolute Value Function. f (x) = . Domain, range, x-intercept, y-intercept, vertex. Exercises: . Sketch the graph of the following and find the domain, range, vertex, and x and y-intercepts: f (x) = . 2. y = . 3. y = . 4. y = + 1.

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