Algebra 2 Online!
Henrico County Public Schools, Virginia
Expressions and Operations

Equations and Inequalities

Functions

Statistics

SOL Review Materials
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
  1. 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 y-intercepts; e) find values of function for elements in domain; f) make connect between/among multiple representation of functions (concrete/verbal/numeric/graphic/algebraic)
  2. 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
  3. SOL AFDA.4 - transfer between/analyze multiple representations of functions (algebraic formulas/ graphs/ tables/words)
Instructional Materials
  1. VDOE ESS Lesson: Inverse Functions  (PDF) - Exploring inverse functions (Word)
  2. Stations: Function Characteristic Card Sort (doc)
Real World Lessons
Practice
Self-Assessments
  1. SOL Mini-Quiz: AII.7g - Functions and their Inverses
Skills
  1. JMU Pivotal Question: Inverse Functions (doc)
  2. JMU Pivotal Question: Inverse Functions of Itself (doc)
Videos
Explore Learning
  1. 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 pre-set 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.
  2. 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 pre-set 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.
  3. 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 pre-set 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
A-SSE.3a
A-APR.3
A-CED.1
F-IF.4
F-IF.7a
F-IF.7c
F-IF.7d
F-IF.7e
F-IF.8a
F-IF.8b
F-IF.9
F-BF.1a
F-BF.1b
F-BF.1c
F-BF.3
F-BF.4
F-BF.5
F-LE.3
F-LE.4
F-LE.5