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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.

Inundated with Inverses: Restricting the Range of an Inverse (Day 1 of 2)

12th Grade Math

Â» Unit:

Basic Functions and Equations

Big Idea:Working with a team, students fold paper to find the inverse of functions they already know and then learn to restrict the range of these inverses to make them functions.

Where are the Functions Farthest Apart? - The Sequel

12th Grade Math

Â» 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.

How do you find the Inverse of a Trigonometric Functions

12th Grade Math

Â» Unit:

Trigonometry as a Real-Valued Functions

Big Idea:Why does my calculator give me a negative angle for sine and tangent when the angle's terminal side is in quadrant II?

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.