Transformations of Linear Functions

Slides:

Advertisements

Similar presentations

Order of function transformations

Advertisements

Parent Functions & Transformations

Essential Question: In the equation g(x) = c[a(x-b)] + d what do each of the letters do to the graph?

Lesson 1-3 New Functions from Old Functions Part 1 - Part 1 tbn3.gstatic.com/images?q=tbn:ANd9GcTMSNbfIIP8t1Gulp87xLpqX92qAZ_vZwe4Q.

Unit 3 Functions (Linear and Exponentials)

Unit 3 Functions (Linear and Exponentials)

Section 3.5 Transformations Vertical Shifts (up or down) Graph, given f(x) = x 2. Every point shifts up 2 squares. Every point shifts down 4 squares.

Objective Transform polynomial functions..

2.4: Transformations of Functions and Graphs

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.

Distributive Property O To distribute and get rid of the parenthesis, simply multiply the number on the outside by the terms on the inside of the parenthesis.

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.

7th Grade Math and Pre-AP Math

Graphing Transformations. It is the supreme art of the teacher to awaken joy in creative expression and knowledge. Albert Einstein.

Graphing Techniques: Transformations

Special Functions. We have come a long way in this module and covered a lot of material dealing with graphs of polynomials. In this lesson we will look.

6-8 Graphing Radical Functions

RULES FOR SIGNED NUMBERS ADDITION And “SUBTRACTION” 1 I have not put in “Animation” to go step-by-step.

Extended Algebra Topics.  We have been combining monomials with monomials ◦ Even when we did 3x x – 11, we were actually only combining monomials.

An absolute-value function is a function whose rule contains an absolute-value expression. The graph of the parent absolute-value function f(x) = |x| has.

Parent Functions and Transformations. Parent Graphs In the previous lesson you discussed the following functions: Linear Quadratic Cubic, Square root.

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

Graph Absolute Value Functions using Transformations

1 10/02/11 Section 1.6 Dr. Mark Faucette Department of Mathematics University of West Georgia.

Chapter 4 Quadratics 4.3 Using Technology to Investigate Transformations.

2.5 Transformations of Functions What are the basic function formulas we have covered and what does each graph look like? What kinds of ways can we manipulate.

1.6 Transformation of Functions

TRANSFORMATIONS Shifts Stretches And Reflections.

Sullivan PreCalculus Section 2.5 Graphing Techniques: Transformations

Graphing Absolute Value Functions using Transformations.

Absolute–Value Functions

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.

Section 1.3 New Functions from Old. Plot f(x) = x 2 – 3 and g(x) = x 2 – 6x + 1 on the same set of axes –What is the relationship between the two 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.

1-3:Transforming Functions English Casbarro Unit 1: Functions.

Transformation of Functions

3.4 Graphs and Transformations

TRANSFORMATIONS OF FUNCTIONS Shifts and stretches.

 How would you sketch the following graph? ◦ y = 2(x – 3) 2 – 8  You need to perform transformations to the graph of y = x 2  Take it one step at a.

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

Parent Functions and Transformations. Transformation of Functions Recognize graphs of common functions Use shifts to graph functions Use reflections to.

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.

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.

2.7 Absolute Value Functions and Transformations Parent Function of Absolute Value  F(x)= I x I  Graph is a “v-shape”  2 rays meeting at a vertex V(0,0)

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.

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

Graphing Techniques: Transformations We will be looking at functions from our library of functions and seeing how various modifications to the functions.

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.

6.5 COMBINING TRANSFORMATIONS 1. Multiple Inside Changes Example 2 (a) Rewrite the function y = f(2x − 6) in the form y = f(B(x − h)). (b) Use the result.

Radical Functions.

Transforming Linear Functions

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.

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

Graphing Techniques: Transformations Transformations: Review

Transformations of Functions

Transformations of Linear Functions

2.4: Transformations of Functions and Graphs

Transformations of Functions and Graphs

Graphic Organizer for Transformations

Transformations of Functions

1.6 Transformations of Functions

Presentation transcript:

Transformations of Linear Functions

The rules and what they mean: This is our function This is our function vertically stretched This is our function vertically compressed This is our function horizontally compressed This is our function horizontally stretched This is our function reflected over the x-axis This is our function reflected over the y-axis

That’s a lot of rules… Now what?! This is our function with a horizontal shift right This is our function with a horizontal shift left This is our function with a vertical shift up This is our function with a vertical shift down That’s a lot of rules… Now what?!

Let’s apply the rules to move functions. y = 3x Let’s start with this function y = 3x shift the function horizontally right 3 horizontal movement will ALWAYS be inside with the x added or subtracted and is OPPOSITE what you want. To move the function horizontally, place the number inside parenthesis and do the opposite of the way you want to move. To move left put a plus and your number and to move right put a minus and your number. y = 3(x – 3)

Let’s try some more! y = 3x horizontal shift left 4 y = 3(x + 4) y = 3x horizontal shift right 5 y = 3(x - 5) y = 3x horizontal shift left 7 y = 3(x + 7)

But what about up and down? y = 3x shift the function vertically up 5 y = 3x + 5 just add on to the end. Remember up you need a + to move up and a – to move down. Vertical movements do EXACTLY what they say. y = 3x shift the function vertically down 2 y = 3x - 2

You try! y = 3x vertical shift up 3 y = 3x + 3 y = 3x vertical shift down 8 y = 3x - 8 Put them together! y = 3x vertical shift down 5 and horizontal shift right 6 y = 3(x – 6) – 5

Too easy? Let’s look at some others! Vertically stretch y = 3x by a scale factor of 2 Simply put the 2 on the outside of 3x like this: y = 2(3x) That’s it???? Yep, that’s it! But what if it is a compression? Same deal but you will see a fraction. Try it! Vertically compress y = 3x by a scale factor of 1/4

Horizontal compressions and stretches the number will be inside touching the x. If the number is a whole number it will COMPRESS If the number is a fraction it will STRETCH the function. y = 3x compress the function horizontally by a scale factor of 2 y = 3(2x)

y = 3x stretch the function horizontally by a scale factor of 1/2 y = 3x reflect across the x-axis y = -3x y = 3x reflect across the y-axis y = 3(-x)