Algebra IITuesday, September 9, 2014A 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 FunctionsTopic: 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: 11-25 odd, 27-28.