Warm Up Wednesday 1. Given this table, what is the slope? XY 14 512 -3-4.

Slides:

Advertisements

Similar presentations

2-6: Families of Functions

Advertisements

Unit 3 Functions (Linear and Exponentials)

Transformations Transforming Graphs. 7/9/2013 Transformations of Graphs 2 Basic Transformations Restructuring Graphs Vertical Translation f(x) to f(x)

Monday, September 15 Algebra II

Section 3.2 Notes Writing the equation of a function given the transformations to a parent function.

Copyright © 2009 Pearson Education, Inc. CHAPTER 2: More on Functions 2.1 Increasing, Decreasing, and Piecewise Functions; Applications 2.2 The Algebra.

Graphical Transformations

Transformation of Functions College Algebra Section 1.6.

Warm UP: Solve and check: 1) 3n – 7 = 262) 3(-4x + 2) = 6(2 + x) Solve and graph each solution on a number line: 3) 5p > 10 or -2p ≤ 10 Solve and check:

LINEAR SYSTEMS – Graphing Method In this module, we will be graphing two linear equations on one coordinate plane and seeing where they intersect. You.

Graphing Reciprocal Functions

Consider the function: f(x) = 2|x – 2| Does the graph of the function open up or down? 2. Is the graph of the function wider, narrower, or the same.

Families of Functions Objective: I can understand transformations of functions. Write in your notebook ONLY what you see in the yellow boxes [except for.

1. 3x + 2 = ½ x – 5 2. |3x + 2| > x – 5 < -3x |x + 2| < 15 Algebra II 1.

Ch 6 - Graphing Day 1 - Section 6.1. Quadratics and Absolute Values parent function: y = x 2 y = a(x - h) 2 + k vertex (h, k) a describes the steepness.

Transformations Transformations of Functions and Graphs We will be looking at simple functions and seeing how various modifications to the functions transform.

2.7 Absolute Value Tranformations

To remember the difference between vertical and horizontal translations, think: “Add to y, go high.” “Add to x, go left.” Helpful Hint.

2.7 Use Absolute Value Functions

1. 3x + 2 = ½ x – 5 2. |3x + 2| > x – 5 < -3x |x + 2| < 15 Algebra II 1.

Holt McDougal Algebra Using Transformations to Graph Quadratic Functions Warm Up For each translation of the point (–2, 5), give the coordinates.

The animation is already done for you; just copy and paste the slide into your existing presentation.

Math-3 Lesson 1-3 Quadratic, Absolute Value and Square Root Functions

FUNCTION TRANSLATIONS ADV151 TRANSLATION: a slide to a new horizontal or vertical position (or both) on a graph. f(x) = x f(x) = (x – h) Parent function.

1. g(x) = -x g(x) = x 2 – 2 3. g(x)= 2 – 0.2x 4. g(x) = 2|x| – 2 5. g(x) = 2.2(x+ 2) 2 Algebra II 1.

QUIZ Wednesday June 10 th (6 questions) Section 1.6 (from ppt) Naming parent functions and writing the domain and range. (3 questions) Graphing functions,

For each function, evaluate f(0), f(1/2), and f(-2)

Section 3-2: Analyzing Families of Graphs A family of graphs is a group of graphs that displays one or more similar characteristics. A parent graph is.

Warm up State the domain and range for: If f(x) = x 3 – 2x +5 find f(-2)

The following are what we call The Parent Functions.

1.5 Graphical Transformations Represent translations algebraically and graphically.

Section 10.1 Day 1 Square Root Functions Algebra 1.

Lesson 3.5 Essential Question: How can you describe the graph of the equation y=mx+b? `Objectives: Finding the slope of a line Finding the slope of a line.

CHAPTER 2: More on Functions

Daily Warm Up Match each function with its graph..

2.6 Families of Functions Learning goals

Transformations of Quadratic Functions (9-3)

College Algebra Chapter 2 Functions and Graphs

Algebra 2 Chapter 2 Part B Review.

Sketch the graph/ Write the equation YoungMath Presents

Using Transformations to Graph Quadratic Functions 5-1

Transformation of Functions

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.

Warm up Using the distance formula, d = , to find the distance between the following sets of points: 1) (2, 5) and (-4, 7) 2)

ALGEBRA II ALGEBRA II HONORS/GIFTED - SECTIONS 2-6 and 2-7 (Families of Functions and Absolute Value Functions) ALGEBRA II HONORS/GIFTED.

Parent Functions and Transformations

Warm Up – August 21, 2017 Find the x- and y-intercepts. X – 3y = 9

Transformations: Review Transformations

5-7 Warm Up – Discovery with Partners

3.4: Graphs and Transformations

Warm Up (3,2), (6,2) (5,6), (-2, -1) (-1, 2), (3, 5)

Parent Functions and Transformations

College Algebra Chapter 2 Functions and Graphs

y x Lesson 3.7 Objective: Graphing Absolute Value Functions.

1.7 Notes: Transformations of Functions

Transforming Linear Functions

2-6 Families of Functions

CHAPTER 2: More on Functions

Transformation of Functions

Horizontal Shift left 4 units Vertical Shift down 2 units

2.4 Symmetry and Transformations

Unit 3 Functions.

Transformation of Functions

The graph below is a transformation of which parent function?

Transformations.

Parent Functions and Transformations

What is the domain and range for the function f(x) =

Warm up honors algebra 2 3/1/19

Presentation transcript:

Warm Up Wednesday 1. Given this table, what is the slope? XY

Transformations

Transformations in Nature

Transformations in Fiction

Transformations in Algebra

How do we Transform a Function?

Parent Function  Basically, parent functions are the function that you start a problem with before transforming it.

Translations  A Translation moves the parent function up/down or left/right.

Linear Transformations  If Kevin can buy a bag of popcorn at the theater for $4, what is his cost for 1, 2, 3 or more bags of popcorn? If Kevin has to buy a ticket for $6 before he can get in the theater, how much will it cost him for 1, 2, 3 or more bags of popcorn?

Vertical Translations If my parent function is f(x) = 4x and h(x) = f(x) + 6 what happens? Take your original equation f(x) and replace it in your h(x) equation so that you get h(x) = 4x + 6 Practice If f(x) = 8x and h(x) = f(x) + 2 what is h(x)? If g(t) = 12t and h(t) = g(t) - 9 what is h(t)? h(x) = 8x + 2 h(t) = 12t - 9

Horizontal Translation If my parent function is f(x) = 4x and h(x) = f(x + 6) what happens? Take your original equation f(x) and replace x with (x + 6) so that you get h(x) = 4(x + 6) = 4x Practice If f(x) = 8x and h(x) = f(x + 2) what is h(x)? If g(t) = 12t and h(t) = g(t - 3) what is h(t)? h(x) = 8(x+2) = 8x + 16 h(t) = 12(t – 3) = 12t - 36

Dilations A dilation makes the function either bigger or smaller. If the number is greater than 1, the function grows, if it is between 0 and 1, the function shrinks.

Vertical Dilation – Altering in the Y Direction h(x) = 16x f(a) = 2a

Horizontal Dilation – Altering in the X Direction

Summary