MCR 3U SECTION 3.4 REFLECTIONS OF FUNCTIONS. Example 1: Graph the functions and on a single grid.

Slides:

Advertisements

Similar presentations

y = ⅔f(x) Vertical Stretches about an Axis.

Advertisements

Objective Transform polynomial functions..

Transformation of Functions Section 1.6. Objectives Describe a transformed function given by an equation in words. Given a transformed common function,

Section 1.6 Transformation of Functions

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

Section 1.7 Symmetry & Transformations

Section 11.2 Notes Writing the equations of exponential and logarithmic functions given the transformations to a parent function.

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

6.5 - Graphing Square Root and Cube Root

Transformations xf(x) Domain: Range:. Transformations Vertical Shifts (or Slides) moves the graph of f(x) up k units. (add k to all of the y-values) moves.

How does one Graph an Exponential Equation?

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.

Transformations We are going to look at some transformation rules today:

College Algebra 2.7 Transformations.

MA 08 transformations 2.3 Reflections. 10/7/ Reflections2 Topic/Objectives Reflection Identify and use reflections in a plane. Understand Line.

REFLECTING GRAPHS AND SYMMETRY

Reflections Section 9.3.

Unit 5 – Linear Functions

Section 2.7 Parent Functions and Transformations

6-8 Graphing Radical Functions

Homework: p , 17-25, 45-47, 67-73, all odd!

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

© Daniel Holloway. Transforming graphs is not too dissimilar from transforming shapes. Whereas you can translate, rotate, reflect and enlarge shapes;

Advanced Algebra II Notes 4.5 Reflections and the Square Root Family

Section 9.5. Composition of Transformations When two or more transformations are combined to form a single transformation, the result is a composition.

Section 1.2 Graphs of Equations in Two Variables.

Test an Equation for Symmetry Graph Key Equations Section 1.2.

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

Notes Over 2.4 Graphs of Common Functions Be Familiar with These Common Functions.

TRANSFORMATIONS Shifts Stretches And Reflections.

Sullivan PreCalculus Section 2.5 Graphing Techniques: Transformations

3.4 Graphing Techniques; Transformations. (0, 0) (1, 1) (2, 4) (0, 2) (1, 3) (2, 6)

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

Copyright © 2011 Pearson, Inc. 1.6 Graphical Transformations.

Transformation of Functions

N18-Reflections With Absolute Value f(x) XY

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

 Let c be a positive real number. Vertical and Horizontal Shifts in the graph of y = f(x) are represented as follows. 1. Vertical shift c upward:

IFDOES F(X) HAVE AN INVERSE THAT IS A FUNCTION? Find the inverse of f(x) and state its domain.

Section 3.5 Graphing Techniques: Transformations.

Reflections Chapter 3 Section 7. Reflections A reflection – is a transformation that flips an image over a line. o This line is called the line of reflection.

EQ: How can transformations effect the graph a parent function? I will describe how transformations effect the graph of a parent function.

PreCalculus Chapter 1 Section 6

Digital Lesson Shifting Graphs.

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

1.3 Combining Transformations

Objective: I can understand transformations of functions.

2.7 – Use of Absolute Value Functions and Transformations.

Review of Transformations and Graphing Absolute Value

Equal distance from origin.

Section 5.1 The Natural Logarithmic Function: Differentiation.

I. There are 4 basic transformations for a function f(x). y = A f (Bx + C) + D A) f(x) + D (moves the graph + ↑ and – ↓) B) A f(x) 1) If | A | > 1 then.

Section 2.4 Symmetry Copyright ©2013, 2009, 2006, 2001 Pearson Education, Inc.

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.

Section 1.4 Transformations and Operations on 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.

1 PRECALCULUS Section 1.6 Graphical Transformations.

Transforming curves

Exponential & Logarithmic functions. Exponential Functions y= a x ; 1 ≠ a > 0,that’s a is a positive fraction or a number greater than 1 Case(1): a >

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

Pre-Cal Chapter 1 Functions and Graphs Section 1.5 Graphical Transformations.

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

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.

Section 1-5 Graphical Transformations. Section 1-5 vertical and horizontal translations vertical and horizontal translations reflections across the axes.

© 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,

Transforming Linear Functions

College Algebra Chapter 2 Functions and Graphs Section 2.6 Transformations of Graphs.

Section P.3 Transformation of Functions. The Constant Function.

Section 1-7 TRANSFORMATIONS OF FUNCTIONS. What do you expect? a)f(x) = (x – 1) Right 1, up 2.

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

Presentation transcript:

MCR 3U SECTION 3.4 REFLECTIONS OF FUNCTIONS

Example 1: Graph the functions and on a single grid

Example 2 : Graph the functions y = x 2 and y = -x 2

If y = f(x), what type of transformation is represented by functions of the form y = -f(x)

In general, if y = f(x), then y = -f(x) represents a reflection in the x-axis

Example 3: Graph the functions and on a single grid

In general, if y = f(x), then y = f(-x) represents a reflection in the y-axis

Invariant points are points that are unaltered by transformations

Example 4: Given f(x) = x 2 – 5x, find f(-x) and –f(x). Determine any invariant points between f(x) and f(-x) and between f(x) and –f(x) for invariant points Invariant point at (0,0)

for invariant points Invariant points at (0,0) and (5,0)