Horizontal Stretches and Compression Lesson 5.4. Manipulating a Function Given the function for the Y= screen y1(x) = 0.1(x 3 – 9x 2 )  Use window -10.

Slides:

Advertisements

Similar presentations

Vertical Stretches and Compressions

Advertisements

Transformation of Graphs Tools for Exploration Consider the function f(x) = 0.1(x 3 – 9x 2 ) Enter this function into your calculator on the y=

Polynomial Functions and Models Lesson 4.2. Review General polynomial formula a 0, a 1, …,a n are constant coefficients n is the degree of the polynomial.

Increasing & Decreasing Functions and 1 st Derivative Test Lesson 4.3.

The Area Between Two Curves

Concavity and Rates of Change Lesson 2.5. Changing Rate of Change Note that the rate of change of the curve of the top of the gate is changing Consider.

Real Zeros of Polynomial Functions Lesson 4.4. Division of Polynomials Can be done manually See Example 2, pg 253 Calculator can also do division Use.

Rates of Change Lesson 3.3. Rate of Change Consider a table of ordered pairs (time, height) 2 TH

Polynomial and Rational Functions

The Area Between Two Curves Lesson When f(x) < 0 Consider taking the definite integral for the function shown below. The integral gives a negative.

Logarithmic Functions and Models Lesson 5.4. A New Function Consider the exponential function y = 10 x Based on that function, declare a new function.

Graphs of Exponential Functions Lesson 3.3. How Does a*b t Work? Given f(t) = a * b t  What effect does the a have?  What effect does the b have? Try.

Curve Sketching Lesson 5.4. Motivation Graphing calculators decrease the importance of curve sketching So why a lesson on curve sketching? A calculator.

Lesson 2.6 Read: Pages Page 152: #1-37 (EOO), 47, 49, 51.

Quadratic Inequalities Lesson Definition Recall the quadratic equation ax 2 + bx + c = 0 Replace = sign with, ≤, or ≥ makes it a quadratic inequality.

Nonlinear Functions and their Graphs Lesson 4.1. Polynomials General formula a 0, a 1, …,a n are constant coefficients n is the degree of the polynomial.

Increasing/ Decreasing

Solving Quadratic Functions Lesson 5.5b. Finding Zeros Often with quadratic functions f(x) = a*x 2 + bx + c we speak of “finding the zeros” This means.

Properties of Functions Section Even, Odd or Neither? 4.

Quadratic Equations and Problem Solving Lesson 3.2.

Antiderivatives Lesson 7.1A. Think About It Suppose this is the graph of the derivative of a function What do we know about the original function? Critical.

Using Derivatives to Sketch the Graph of a Function Lesson 4.3.

Sign Studies. Why do we use sign studies? Example 1. Determine the equation of f(x) by identifying the x-intercepts (roots, solutions, zeros, factors)

The Natural Log Function: Integration Lesson 5.7.

Solve by Factoring Zero Product Property.

Quadratic Functions, Translation and Reflection

Section Equivalent Transformations. Lesson Objective: Students will: Understand that a vertical stretch of y = x² is equivalent to a horizontal.

College Algebra 2.4 Properties of Functions Objectives: 1. Determine even or odd functions 2. Determine behavior of a function. 3. Find local min and max.

Polynomial Functions Lesson 9.2. Polynomials Definition:  The sum of one or more power function  Each power is a non negative integer.

Vertical Stretches and Compressions Lesson 6.3. Sound Waves Consider a sound wave  Represented by the function y = sin (x) Place the function in your.

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.

Short Run Behavior of Polynomials

Shifting a Function’s Graph

The Area Between Two Curves

Increasing, Decreasing, Constant

Polynomial Functions Lesson 11.2.

Quadratic Equations and Problem Solving

Real Zeros of Polynomial 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.

Short Run Behavior of Polynomials

Polynomial and Rational Functions

Nonlinear Functions and their Graphs

Curve Sketching Lesson 5.4.

Quadratic Inequalities

Vertical Stretches and Compressions

Polynomial Functions and Models

Quadratic Functions, Translation and Reflection

Rates of Change Lesson 3.3.

The Area Between Two Curves

Horizontal Stretches and Compression

Short Run Behavior of Polynomials

Concavity and Second Derivative Test

Reflections and Symmetry

Shifting a Function’s Graph

Transformation of Graphs

Exponential Functions

Polynomial Functions Lesson 9.2.

Parent Functions and Transformations

For each table, decide if y’is positive or negative and if y’’ is positive or negative

7.2 Polynomial Functions and Their Graphs

7.2 Graphing Polynomial Functions

For each table, decide if y’is positive or negative and if y’’ is positive or negative

Pre-Calculus Go over homework End behavior of a graph

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

(3, 2) 2 -3 (-4, -3) -2 (5, -2) 1. a) Find: f(3) = ______

15 – Transformations of Functions Calculator Required

1.7 Transformations of Functions

Sec 4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH

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

Concavity and Rates of Change

Presentation transcript:

Horizontal Stretches and Compression Lesson 5.4

Manipulating a Function Given the function for the Y= screen y1(x) = 0.1(x 3 – 9x 2 )  Use window -10 < x < 10 and -20 < y < 20 Now do the transformation  y2(x) = y1(.5x)  y3(x) = y1(3x) Make predictions for what will happen Set the styles different

Manipulating a Function For  Horizontal stretch  Horizontal compression Original f(x) 0 < a < 1 a > 1 f(0.5x) stretched f(3x) compressed

Changes to a Graph Consider once again the effect of modifiers For this lesson we are concentrating on b b => horizontal stretch/compression  b > 1 causes compression  |b| < 1 causes stretching

Changes to a Table Try these functions  y1(x) = 3x 2 – 2x  y2(x) = y1(0.5 x)  y3(x) = y1(2x) Go to tables (  Y), then setup, F2  Table start = - 4  Table increment = 1

Changes to a Table Note the results f(x) f(0.5x) f(2x) Stretched Compressed

Changes to a Graph View the different versions of the altered graphs What has changed? What remains the same? What has changed? What remains the same?

Changes to a Graph Classify the following properties as changed or not changed when the function f(x) is modified by a coefficient f(b*x) PropertyChanged Not Changed Zeros of the function Intervals where the function increases or decreases X locations of the max and min Y-locations of the max and min Steepness of curves where function is increasing/decreasing

Functions Where Formula Not Known Given a function defined by a table  Fill in all possible blanks x f(x) f(.5x) f(2x)

Functions Where Formula Not Known Given f(x) defined by graph below Which is f(2x)? 2*f(x)? f(0.5x)?

Assignment Lesson 5.4 Page 223 Exercises 1 – 27 odd