Vocabulary A nonlinear function that can be written in the standard form Cubic Function 3.1Graph Cubic Functions A function where f (  x) =  f (x).

Slides:

Advertisements

Similar presentations

Lesson 3.1 Graph Cubic Functions Goal Graph and analyze cubic functions.

Advertisements

Unit 3 Functions (Linear and Exponentials)

2.7: Use Absolute Value Functions and Transformations

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

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.

Transforming reciprocal functions. DO NOW Assignment #59  Pg. 503, #11-17 odd.

Section 1.7 Symmetry & Transformations

Vertical shifts (up) A familiar example: Vertical shift up 3:

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 to Parent Functions. Translation (Shift) A vertical translation is made on a function by adding or subtracting a number to the function.

Determine whether a graph is symmetric with respect to the x-axis, the y-axis, and the origin. Determine whether a function is even, odd, or neither even.

College Algebra 2.7 Transformations.

Shifting Graphs Digital Lesson. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 The graphs of many functions are transformations.

Reflections, Transformations and Interval Notation L. Waihman Revised 2006.

Apply rules for transformations by graphing absolute value functions.

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

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

Special Functions and Graphs Algebra II …………… Sections 2.7 and 2.8.

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.

Objective: To us the vertex form of a quadratic equation 5-3 TRANSFORMING PARABOLAS.

Unit 6 Lesson 8. Do Now Find the following values for f(x) and g(x): f(x) = x 2 g(x) = 2x 2 f(1); f(2); f(0); f(-1); f(-2) g(1); g(2); g(0); g(-1); g(-2)

Pre-Calculus Lesson 3: Translations of Function Graphs Vertical and horizontal shifts in graphs of various functions.

MAT 150 Algebra Class #12 Topics: Transformations of Graphs of Functions Symmetric about the y- axis, x-axis or origin Is a function odd, even or neither?

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.

2.5 Transformations and Combinations of Functions.

3.4 Graphs and Transformations

Graphing Rational Functions Through Transformations.

2.7 Absolute Value Tranformations

 Determine the value of k for which the expression can be factored using a special product pattern: x 3 + 6x 2 + kx + 8  The “x” = x, and the “y” = 2.

2.8 Absolute Value Functions

Section 3.5 Graphing Techniques: Transformations.

Copyright © Cengage Learning. All rights reserved. Pre-Calculus Honors 1.3: Graphs of Functions HW: p.37 (8, 12, 14, all, even, even)

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

Math 1111 Test #2 Review Fall Find f ° g.

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) Why is the origin the most important point on every graph? 2) What are THREE different ways you can get from the origin to point “P”?

Transformations of Linear and Absolute Value Functions

 A function that can be expressed in the form and is positive, is called an Exponential Function.  Exponential Functions with positive values of x are.

Parent Graphs and Transformations

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)

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|.

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.

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.

5.8 Graphing Absolute Value Functions I can graph an absolute value function and translate the graph of an absolute value function.

Section 1.4 Transformations and Operations on Functions.

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

TODAY IN CALCULUS…  Learning Targets :  You will be able to graph and transform an absolute value function.  You will be able to write and evaluate.

Find a Function Value Write original function. Example 1 1.7Graph Linear Functions Substitute ____ for x. Simplify.

ODD FUNCTIONS What is their common characteristic? They have point symmetry about the origin.

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

RECAP Functions and their Graphs. 1 Transformations of Functions For example: y = a |bx – c| + d.

Ch. 1 – Functions and Their Graphs 1.4 – Shifting, Reflecting, and Sketching Graphs.

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.

Transformationf(x) y = f(x) + c or y = f(x) – c up ‘c’ unitsdown ‘c’ units EX: y = x 2 and y = x F(x)-2 xy F(x) xy

Transforming Linear Functions

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

The following are what we call The Parent Functions.

Shifting, Reflecting, & Stretching Graphs 1.4. Six Most Commonly Used Functions in Algebra Constant f(x) = c Identity f(x) = x Absolute Value f(x) = |x|

2.4 Transformations of Functions

Rev Graph Review Parent Functions that we Graph Linear:

Section 1.6 Transformation of Functions

y x Lesson 3.7 Objective: Graphing Absolute Value Functions.

REFLECTIONS AND SYMMETRY

The graph below is a transformation of which parent function?

Presentation transcript:

Vocabulary A nonlinear function that can be written in the standard form Cubic Function 3.1Graph Cubic Functions A function where f (  x) =  f (x). The graph is symmetric about the origin. Odd Function A function where f (  x) = f (x). The graph is symmetric about the y-axis. Even Function The behavior of a function’s graph as x approaches positive infinity or negative infinity. End Behavior

Graph of the Parent Function For Absolute Value Functions 1.9Graph Absolute Value Functions Comparing Graphs of Absolute Value Functions with the Graph of f (x) = |x| The graph of g is a ___________ shift of the graph of f (x) = |x|. The shift is h units __________ if h > 0 and |h| units _______ if h < 0. The graph of h hh h (x) = |x + h| is a ______________ in the y-axis of the graph of g. horizontal right left reflection

Graph of the Parent Function For Absolute Value Functions 1.9Graph Absolute Value Functions Comparing Graphs of Absolute Value Functions with the Graph of f (x) = |x| The graph of g is a ___________ shift of the graph of f (x) = |x|. The shift is k units __________ if k > 0 and |k| units _______ if k < 0. vertical up down

Graph of the Parent Function For Absolute Value Functions 1.9Graph Absolute Value Functions Comparing Graphs of Absolute Value Functions with the Graph of f (x) = |x| If |a| > 1, the graph of g is a vertical _________ of the graph of f (x) = |x|. If 0 < |a| <1, the graph of g is a vertical ________ of the graph of (x) = |x|. The graph of h (x) = a |x | is a ____________ in the x-axis of the graph of g. stretch shrink reflection

1.9Graph Absolute Value Functions Example 1 Compare the graph with the graph of f (x) = |x|. Make a table of values. Graph the function. Compare the graphs of g and f. x g(x)g(x) a. The graph of g(x) = |x + 1| is a ______________________________ of the graph of f (x) = |x|. horizontal shift 1 unit to the left

1.9Graph Absolute Value Functions Example 1 Compare the graph with the graph of f (x) = |x|. Make a table of values. Graph the function. Compare the graphs of g and f. x g(x)g(x) b. The graph of g(x) = |x|  2 is a ___________________________ of the graph of f (x) = |x|. vertical shift 2 units down

1.9Graph Absolute Value Functions The graph of g is a ___________________________ of the graph of f. horizontal shift 3 units to the right Checkpoint. Graph the function. Compare the graph with the graph of f (x) = |x|.

1.9Graph Absolute Value Functions The graph of g is a ____________________ of the graph of f. vertical shift 2 units up Checkpoint. Graph the function. Compare the graph with the graph of f (x) = |x|.

1.9Graph Absolute Value Functions Example 2 Compare the graph with the graph of f (x) = |x|. Make a table of values. Graph the function. Compare the graphs of g and f. x g(x)g(x) a. The graph of g(x) =  2 |x| opens ______ and is a ________________ of the graph of f (x) = |x|. down vertical stretch

1.9Graph Absolute Value Functions Example 2 Compare the graph with the graph of f (x) = |x|. Make a table of values. Graph the function. Compare the graphs of g and f. x g(x)g(x) b. The graph of g(x) =  2 |x| opens ______ and is a ________________ of the graph of f (x) = |x|. up vertical shrink

1.9Graph Absolute Value Functions Checkpoint. Graph the function. Compare the graph with the graph of f (x) = |x|. The graph of g opens up and is a vertical stretch of the graph of f.

1.9Graph Absolute Value Functions Checkpoint. Graph the function. Compare the graph with the graph of f (x) = |x|. The graph of g opens down and is a vertical shrink of the graph of f.

1.9Graph Absolute Value Functions