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

Slides:

Advertisements

Similar presentations

Order of function transformations

Advertisements

Parent Function Transformation Students will be able to find determine the parent function or the transformed function given a function or graph.

Sec. 3.2: Families of Graphs Objective: 1.Identify transformations of graphs studied in Alg. II 2.Sketch graphs of related functions using transformations.

Objective Transform polynomial functions..

The vertex of the parabola is at (h, k).

Essential Question: In the equation f(x) = a(x-h) + k what do each of the letters do to the graph?

Table of Contents Functions: Transformations of Graphs Vertical Translation: The graph of f(x) + k appears.

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

Relations and Functions Linear Equations Vocabulary: Relation Domain Range Function Function Notation Evaluating Functions No fractions! No decimals!

I can graph and transform absolute-value functions.

1 The graphs of many functions are transformations of the graphs of very basic functions. The graph of y = –x 2 is the reflection of the graph of y = x.

6-8 Transforming Polynomial Functions Warm Up Lesson Presentation

Lesson 9-3: Transformations of Quadratic Functions

Section 2.7 Parent Functions and Transformations

1.6 PreCalculus Parent Functions Graphing Techniques.

6-8 Graphing Radical Functions

3-8 transforming polynomial functions

2.7 Graphing Absolute Value Functions The absolute value function always makes a ‘V’ shape graph.

Graphing Reciprocal Functions

8-2 Properties of Exponential Functions. The function f(x) = b x is the parent of a family of exponential functions for each value of b. The factor a.

© The Visual Classroom 3.7 Transformation of Functions Given y = f(x), we will investigate the function y = af [k(x – p)] + q for different values of a,

Sullivan PreCalculus Section 2.5 Graphing Techniques: Transformations

Graphing Absolute Value Functions using Transformations.

Absolute–Value Functions

3-2 Families of Graphs Pre Calc A. Parent Graphs.

Graph and transform absolute-value functions.

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

Graphical Transformations. Quick Review What you’ll learn about Transformations Vertical and Horizontal Translations Reflections Across Axes Vertical.

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.

Section 3.5 Graphing Techniques: Transformations.

The absolute-value parent function is composed of two linear pieces, one with a slope of –1 and one with a slope of 1. In Lesson 2-6, you transformed linear.

2.5 Shifting, Reflecting, and Stretching Graphs. Shifting Graphs Digital Lesson.

Transformation of Functions Sec. 1.7 Objective You will learn how to identify and graph transformations.

1.3 Combining Transformations

Objective: I can understand transformations of functions.

Warm Up Give the coordinates of each transformation of (2, –3). 4. reflection across the y-axis (–2, –3) 5. f(x) = 3(x + 5) – 1 6. f(x) = x 2 + 4x Evaluate.

Review of Transformations and Graphing Absolute Value

Vocabulary The distance to 0 on the number line. Absolute value 1.9Graph Absolute Value Functions Transformations of the parent function f (x) = |x|.

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.

Chapter Exploring Transformations

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

Section 9.3 Day 1 Transformations of Quadratic Functions

Section 1.4 Transformations and Operations on Functions.

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,

2.6 Families of Functions Sets of functions, called families, in what each function is a transformation of a special function called the parent. Linear.

HPC 2.5 – Graphing Techniques: Transformations Learning Targets: -Graph functions using horizontal and vertical shifts -Graph functions using reflections.

The base e P 667. Essential Question How is the graph of g(x) = ae x – h + k related to the graph of f(x) = e x.

Section 2.5 Transformations Copyright ©2013, 2009, 2006, 2001 Pearson Education, Inc.

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

Warm-Up Evaluate each expression for x = -2. 1) (x – 6) 2 4 minutes 2) x ) 7x 2 4) (7x) 2 5) -x 2 6) (-x) 2 7) -3x ) -(3x – 1) 2.

5-3 Using Transformations to Graph Quadratic Functions.

Transforming Linear Functions

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.

Transforming Linear Functions

2.6 Families of Functions Learning goals

Transformations of Quadratic Functions (9-3)

Find the x and y intercepts.

Absolute Value Transformations

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.

Absolute Value Functions

2.6 Translations and Families of Functions

Parent Functions and Transformations

The vertex of the parabola is at (h, k).

LEARNING GOALS FOR LESSON 2.6 Stretches/Compressions

15 – Transformations of Functions Calculator Required

Transformations.

Replacing with and (2.6.2) October 27th, 2016.

Warm up honors algebra 2 3/1/19

Presentation transcript:

Families of Functions Objective: I can understand transformations of functions. Write in your notebook ONLY what you see in the yellow boxes [except for this yellow box ]. Everything will be done on your graphing calculator today.

Vocabulary Parent Function Simplest form in a set of functions. Transformation: Change in the size or position of a function Translation: Moves a function horizontally or vertically Reflection: Reflects a function across a line of reflection Dilation: Changes a function size

Set your calculator window to: Graph Translations Vertical Translation: k units Up:Down: xy1y1 y2y

Graph Translations Horizontal Translation, h units Left:Right: xy1y1 y2y

Reflections Graph Reflections: Across x-axis Across y-axis xy1y1 y2y xy1y1 y3y3 -2error1.4 error error

Dilations: Vertical stretchcompression Dilations Graph xy1y1 y2y

Transformation of f(x) Translation: Vertical (k > 0) Translation: Horizontal (k > 0) Dilation: Vertical by a factor of a Reflection Up k units Down k units Right h units Left h units Stretch: Compression: Across x-axis Across y-axis

Combining Transformations Find g(x) when f(x) is translated 2 units left. Find g(x) when f(x) is translated 3 units up. Find g(x) when f(x) is stretched by a factor of 0.5 and reflected across the y-axis. p.104:10-33