Chapter 2 Section 2.7 Graphing Techniques. Multiplying the Function or the Independent Variable by a Number.

Slides:

Advertisements

Similar presentations

Section 2.5 Transformations of Functions. Overview In this section we study how certain transformations of a function affect its graph. We will specifically.

Advertisements

Sullivan Algebra and Trigonometry: Section 2.2 Graphs of Equations Objectives Graph Equations by Plotting Points Find Intercepts from a Graph Find Intercepts.

2.2 Graphs of Equations in Two Variables Chapter 2 Section 2: Graphs of Equations in Two Variables In this section, we will… Determine if a given ordered.

Section 1.7 Symmetry & Transformations

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.

Copyright © 2009 Pearson Education, Inc. CHAPTER 2: More on Functions 2.1 Increasing, Decreasing, and Piecewise Functions; Applications 2.2 The Algebra.

Transformation of Functions College Algebra Section 1.6.

3.1 Solving equations by Graphing System of equations Consistent vs. Inconsistent Independent vs. Dependent.

Section 1.2 Graphs of Equations in Two Variables.

Symmetry Two points, P and P ₁, are symmetric with respect to line l when they are the same distance from l, measured along a perpendicular line to l.

Determine if the following point is on the graph of the equation. 2x – y = 6; (2, 3) Step 1: Plug the given points into the given equation. 2(2) – (3)

SYMMETRY, EVEN AND ODD FUNCTIONS NOTES: 9/11. SYMMETRY, EVEN AND ODD FUNCTIONS A graph is symmetric if it can be reflected over a line and remain unchanged.

Test an Equation for Symmetry Graph Key Equations Section 1.2.

Copyright © 2011 Pearson, Inc. 1.6 Graphical Transformations.

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

Trigonometry/ Pre-Calculus Chapter P: Prerequisites Section P.5: Solving Inequalities Algebraically and Graphically.

Notes Over 10.6 Writing an Equation of a Translated Parabola Write an equation for the parabola.

Symmetry & Transformations

Chapter 4: Systems of Equations and Inequalities Section 4.3: Solving Linear Systems Using Graphs.

Section 1.2 Graphs of Equations In Two Variables; Intercepts; Symmetry.

2.7 Absolute Value Functions and Graphs The absolute value of x is its distance from 0, the absolute value of f(x), or |f(x)|, gives the distance from.

Warm-up . What do we need to keep the same? What do we need to change?

1 PRECALCULUS Section 1.6 Graphical Transformations.

Section 2.4. X-axis: replace y with –y. Simplify. If you get an equation = to what you started with, the function is symmetric to the x-axis. Y-axis:

Chapter 4: Polynomials Quadratic Functions (Section 4.1)

Chapter 3 Section 3.3 Linear Functions: Graphs and Applications.

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

CHAPTER 2: More on Functions

2.1Intercepts;Symmetry;Graphing Key Equations

2.2 Graphs of Equations.

Section 3.5 – Transformation of Functions

Objective: Test for symmetry in polar equations.

Graphs of Equations in Two Variables

Graphing Techniques Transformations

Transformations of Functions

WARM UP Use the graph of to sketch the graph of

Lesson 2-6 Families of Functions.

Graphing Technique; Transformations

Section 6.4 Graphs of Polar Equations

Transformation of Functions

Chapter 2: Functions, Equations, and Graphs

Graphs of Equations In Two Variables; Intercepts; Symmetry

Sullivan Algebra and Trigonometry: Section 2.2

Parabolas 4.2. Parabolas 4.2 Standard Form of Parabolic Equations Standard Form of Equation Axis of Symmetry Vertex Direction Parabola Opens up or.

Chapter 1: Lesson 1.2 Graphs of Equations

Pre-AP Pre-Calculus Chapter 1, Section 6

Notes Over 1.1 To check for y-axis symmetry replace x with -x.

Section 2.4 Symmetry.

Quadratic Functions and Equations

Objective: To solve systems of second degree equations

Find the x-coordinate of the vertex

Focus of a Parabola Section 2.3.

Chapter 2: Analysis of Graphs of Functions

Notes Over 6.4 Graph Sine, Cosine Functions.

Graphical Transformations

Graphs of Equations Objectives: Find intercepts from a Graph

1.3 Symmetry; Graphing Key Equations; Circles

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

CHAPTER 2: More on Functions

Transformation of Functions

Transformations of Functions

B’ (-18, 20) A’ (-21, 4) T’ (13, -11) Translate (x – 9, y + 8)

Graphing Techniques Transformations

Chapter 2 More on Functions.

2.4 Symmetry and Transformations

Determining the Function Obtained from a Series of Transformations.

Graphs of Equations Objectives: Find intercepts from a Graph

Graphing Key Equations

1-6: Absolute Value Equations

Objective: Test for symmetry in polar equations.

Presentation transcript:

Chapter 2 Section 2.7 Graphing Techniques

Multiplying the Function or the Independent Variable by a Number

Symmetry about the x and y Axes A graph is symmetric about the y -axis if you reflect is graph about the y -axis it dos not change this means that: Replacing y by – y in the equation does not change the equation! This is symmetric about the x -axis This is not symmetric about the x -axis This is symmetric about the y -axis This is not symmetric about the y -axis

Multiplying the Function or the Independent Variable by a Number

Translating a Function Left or Right

Translating a Function Up or Down

Combining Graphical Operations