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- HSF-BF.B.3Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
- HSF-BF.B.4Find inverse functions.
- HSF-BF.B.5(+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

Finding the Inverse of a Function Day 1 of 2

12th Grade Math

» Unit:

Functions and Piecewise Functions

Big Idea:By reading and discussing a mathematical text, a process for finding inverses will be uncovered.

Which Came First the Chicken or the Egg? Inverse Functions

Algebra I

» Unit:

Thinking Like a Mathematician: Modeling with Functions

Big Idea:Students construct their own understanding of inverse functions through an exploratory function sort!

What Does "a" Do?

Algebra I

» Unit:

Quadratic Functions

Big Idea:Starting with today's assignment, my classroom becomes a workshop. Every student will learn as much as they can between now and the end of the unit.

Inverse Trig Functions - Day 1 of 2

12th Grade Math

» Unit:

Trigonometric Functions

Big Idea:Use a graphical perspective to establish inverse trig functions.

Review Day

12th Grade Math

» Unit:

Basic Functions and Equations

Big Idea:This lesson, driven by a 3-2-1 assessment, helps students to review past learning and continue to make new connections.

FInal Discussion - "Demystifying e" PLUS Skills Practice with Logarithms

Algebra II

» Unit:

Exponential and Logarithmic Functions

Big Idea:This lesson builds on the “concept level” understanding that the students have obtained on “e” and extends that knowledge to skills practice and the natural logarithm function. It also focuses on mathematics specific readings strategies.

Compositions, Inverses & Role Play: Extending Concepts to Exponential Functions

Algebra II

» Unit:

Exponential and Logarithmic Functions

Big Idea:This lesson welcomes the students back from spring break with a transition to inverse functions. The element of “role play” helps to set the stage for the foundation of logarithms

Inundated with Inverses: Algebraic Inverse and Composition to Verify (Day 2 of 2)

12th Grade Math

» Unit:

Basic Functions and Equations

Big Idea:Students build on intuitive process of finding inverses to develop an algebraic process then explore how composition of functions relates to inverses.

Test Review

12th Grade Math

» Unit:

Basic Functions and Equations

Big Idea:Students work together to review for the upcoming test.

Algebra II Jeopardy

Algebra II

» Unit:

Games

Big Idea:Play Jeopardy to fill those odd days before break or during homecoming week with meaningful mathematical activities like this Jeopardy game.

Inverse Functions

Algebra II

» Unit:

Modeling with Functions

Big Idea:Extend beyond the skill of finding an inverse function to understanding their purpose through real life scenarios.

Unit Review Game: Trashball

12th Grade Math

» Unit:

Functioning with Functions

Big Idea:Use Trashball to review the important concepts of this unit.

Operations with Rational Expressions

Algebra II

» Unit:

Rational and Inverse Functions

Big Idea:Operations with rational expressions are just like operations with fractions.

Functioning with Functions: Unit Assessment

12th Grade Math

» Unit:

Functioning with Functions

Big Idea:Assess students' understanding of functions.

Where are the Functions Farthest Apart? - The Sequel

12th Grade Math

» Unit:

Functioning with Functions

Big Idea:Inverses, combinations of functions, and maximization are all essential to solve a problem about horizontal distance on a graph.

HSF-BF.B.4a

Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2 x^{3} or f(x) = (x+1)/(x–1) for x ≠ 1.

HSF-BF.B.4b

(+) Verify by composition that one function is the inverse of another.

HSF-BF.B.4c

(+) Read values of an inverse function from a graph or a table, given that the function has an inverse.

HSF-BF.B.4d

(+) Produce an invertible function from a non-invertible function by restricting the domain.