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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.

- HSF-BF.B.4aSolve 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<sup>3</sup> or f(x) = (x+1)/(xâ1) for x â 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.

Finding the Inverse of a Function Day 2 of 2

12th Grade Math

Â» Unit:

Functions and Piecewise Functions

Big Idea:Students use composition to justify that two functions are inverses.

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

12th Grade Math

Â» 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

Â» Unit:

Basic Functions and Equations

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

Assessment

12th Grade Math

Â» Unit:

Functions and Piecewise Functions

Big Idea:Students demonstrate competency on working with functions on a written assessment.

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)/(xâ1) for x â 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.