AII.7gh 
The student will investigate and analyze functions algebraically and graphically. Key concepts include
g) inverse of a function;
Graphing calculators will be used as a tool to assist in investigation of functions. 

Essential Knowledge and Skills 
 Find the inverse of a function.
 Graph the inverse of a function as a reflection across the line y = x.
 Investigate exponential and logarithmic functions, using the graphing calculator.
 Convert between logarithmic and exponential forms of an equation with bases consisting of natural numbers.

Essential Understandings 
 If (a, b) is an element of a function, then (b, a) is an element of the inverse of the function.
 Exponential (y=a^x) and logarithmic (y=logax) functions are inverses of each other.


Vertical Articulation 
 SOL A.7  investigate/analyze function (linear/ quadratic) families and characteristics (algebraically/graphically) ‐ a) determine relation is function; b) domain/range;
c) zeros; d) x‐ and yintercepts; e) find values of function for elements in domain; f) make connect between/among multiple representation of functions (concrete/verbal/numeric/graphic/algebraic)
 SOL AFDA.1  investigate/analyze function (linear/quadratic exponential/log) families/ characteristics: a) continuity; b) local/abs max/min;
c) domain/range; d) zeros; e) intercepts; f) intervals of increasing/ decreasing; g) end behaviors; h) asymptotes
 SOL AFDA.4  transfer between/analyze multiple representations of functions (algebraic formulas/ graphs/ tables/words)

Instructional Materials 
 VDOE ESS Lesson: Inverse Functions (PDF)  Exploring inverse functions (Word)
 Stations: Function Characteristic Card Sort (doc)

Real World Lessons 

Practice 

SelfAssessments 
 SOL MiniQuiz: AII.7g  Functions and their Inverses

Skills 
 JMU Pivotal Question: Inverse Functions (doc)
 JMU Pivotal Question: Inverse Functions of Itself (doc)

Videos 

Explore
Learning 
 Function Machines 1 (Functions and Tables)  Drop a number into a function machine, and see what number comes out! You can use one of the six preset function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph.
 Function Machines 2 (Functions, Tables, and Graphs)  Drop a number into a function machine, and see what number comes out! You can use one of the six preset function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph.
 Function Machines 3 (Functions and Problem Solving)  Drop a number into a function machine, and see what number comes out! You can use one of the six preset function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph.

Websites 

Common Core
Standards 
ASSE.3a 
AAPR.3 
ACED.1 
FIF.4 
FIF.7a 
FIF.7c 
FIF.7d 
FIF.7e 
FIF.8a 
FIF.8b 
FIF.9 
FBF.1a 
FBF.1b 
FBF.1c 
FBF.3 
FBF.4 
FBF.5 
FLE.3 
FLE.4 
FLE.5 
