Algebra II Tuesday, September 9, 2014 A Day  Drill: Graph triangle ABC with points A(1, 3), B(5, 6), and C(7, 1). Identify the points of the image of.

Slides:

Advertisements

Similar presentations

Common Core Mathematical Practices. People who are good in math… Make sense of problems.

Advertisements

Standards for Mathematical Practice

Quadratic Techniques to Solve Polynomial Equations CCSS: F.IF.4 ; A.APR.3.

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

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.

4.4 Transformations with Matrices

Section 1.7 Symmetry & Transformations

4.3 Reflecting Graphs; Symmetry In this section and the next we will see how the graph of an equation is transformed when the equation is altered. This.

Preview of Calculus.

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.

Chapter 3: Transformations of Graphs and Data Lesson 4: Symmetries of Graphs Mrs. Parziale.

Symmetry and Coordinate Graphs Symmetry and Coordinate Graphs Section 3-1 How do we determine symmetry using algebra? How do we classify functions as even.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–1) CCSS Then/Now New Vocabulary Example 1:Identify Linear Functions Example 2:Real-World Example:

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

1.2 Graphs of Equations. Objective Sketch graphs of equations Find x and y intercepts of graphs of equations Use symmetry to sketch graphs of equations.

1.2: Functions and Graphs. Relation- for each x value, there can be any y-values. Doesn’t pass the VLT. (ex. (1,2), (2,4), (1,-3) Function- For each x-value,

Domains & Ranges I LOVE Parametric Equations Operations of Functions Inverse Functions Difference.

Advanced Algebra II Notes 4.5 Reflections and the Square Root Family

3.1 Symmetry; Graphing Key Equations. Symmetry A graph is said to be symmetric with respect to the x-axis if for every point (x,y) on the graph, the point.

3-1 Symmetry and Coordinate Graphs Pre Calc A. Point Symmetry Symmetric about the origin: any point in Quadrant I has a point in Quadrant III (rotate.

Symmetry and Coordinate Graphs

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.

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?

3-1 Symmetry & Coordinate Graphs Objective: 1. To determine symmetry of a graph using algebraic tests. 2. To determine if a function is even or odd.

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.

3-1 Symmetry and Coordinate Graphs. Graphs with Symmetry.

Pre-calc section 4-3 Reflections and symmetry part II.

Chapter 1 Functions and Their Graphs

Test an Equation for Symmetry Graph Key Equations Section 1.2.

1. 2 MATHEMATICAL REASONING INSTITUTE LESSON GOALS 3  A.5.e – For a function that models a linear or nonlinear relationship between two quantities,

Objectives: Explore features of the absolute-value function. Explore basic transformations of the absolute-value function. Standards Addressed: O:

Over Lesson 2–1 5-Minute Check 1 Determine whether the relation is a function. If it is a function, determine if it is one-to-one, onto, both, or neither.

Warm-up Express using radicals.. Understanding Symmetry and Its Relationship to Even and Odd Functions.

Q1: Student has difficulty starting You are given two pieces of information. Which form of a quadratic equation can you match the information to? Q2: Student.

Objective: Students will be able to represent translations, dilations, reflections and rotations with matrices.

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

Essential Question: How do we decide for the degree of the polynomial with a variable? How do we determine the end behavior of a polynomial function?

Unit 1: Functions Minds On What do you think of when you hear “inverse”?

Today in Pre-Calculus Go over homework Notes: Symmetry –Need a calculator Homework.

Coordinate Algebra Day 75

Lesson 1.6 Inverse Functions. Inverse Function, f -1 (x): Domain consists of the range of the original function Range consists of the domain of the original.

Graphs of Equations Objective: To use many methods to sketch the graphs of equations.

Splash Screen. CCSS Content Standards F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables.

Example 1 Estimate Function Values A. ADVERTISING The function f (x) = –5x x approximates the profit at a toy company, where x represents marketing.

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

1.4 Functions and Inverses Move to page 1.2Grab and drag point P. What changes and what remains the same? Record some ordered pairs for point P and point.

1. 2 MATHEMATICAL REASONING INSTITUTE LESSON GOALS 3  A.5.e – For a function that models a linear or nonlinear relationship between two quantities,

Warm up 1. Give an example of an even function? 2. Give and example of an odd function? 3. Graph y = x

4.3 Symmetry Objective To reflect graphs and use symmetry to sketch graphs. Be able to test equations for symmetry. Use equations to describe reflections.

WARM UP Evaluate 1. and when and 2. and when and.

Review Chapter 1 Functions and Their Graphs. Lines in the Plane Section 1-1.

Algebra I Exponential Functions: The Marvel of Medicine Irina Keith.

WARM UP Evaluate 1. and when and 2. and when and.

Graphing Quadratic Functions

Warmup: Find the inverse function for each:

Mod 1.2: Characteristics of Function Graphs

4.3 Symmetry Which graph is NOT a function?

All other materials should be on the floor or in a desk.

The relation between the fuel economy and speed of a given car was recorded. What is the fuel economy at 20mph? Problem of the Day f(20) = 15 c)

Power Functions Investigating symmetry to determine if a power function is even, odd, or neither.

Relations P.O.D. #34 Feb 18 Find each function value.

Classify functions as even or odd.

What is the slope of the line?

Five-Minute Check (over Lesson 2–1) Mathematical Practices Then/Now

Presentation transcript:

Algebra II Tuesday, September 9, 2014 A Day  Drill: Graph triangle ABC with points A(1, 3), B(5, 6), and C(7, 1). Identify the points of the image of triangle ABC given the following transformations:  Reflection over the y-axis  Reflection over the x-axis  Reflection over the line y=x  Rotation of 180° about the origin

Unit I: Intro to Families of Functions Topic: Symmetry and Inverses  Objective: Students will… For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal description). Find inverse functions.  Standards for Math Practices Used: MP3: Construct viable arguments and critique the reasoning of others. MP4: Model with mathematics. MP5: Use appropriate tools strategically. MP6: Attend to precision. MP7: Look for and make use of structure.

Exploring Symmetry  Break into four groups. Make groups as even as possible.  Complete the Exploring Symmetry activity.  Now, break into smaller groups containing one member from each of the larger four groups. Report your findings to the new group and compare the different transformations for the same original function.

Even and Odd Functions  Even functions A function is even if its graph is symmetric with respect to the y-axis. f(-x)=f(x)  Odd functions A function is odd if its graph is symmetric with respect to the origin (rotational symmetry of 180°). f(-x)= -f(x)

Inverses of Functions  Look at the reflection in the line y=x. The transformed image under this reflection is called he inverse.  For which graphs did the inverse produce another function?  Identify any relationship you see between the original functions and their inverses.  Inverse of a Relation: The inverse of a relation consisting of the ordered pairs (x, y) is the set of all ordered pairs (y, x). Domain of the inverse=range of original relation Range of inverse=domain of original relation

Homework  p. 122: odd,