Algebra 2 Online!
Henrico County Public Schools, Virginia
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AII.6
The student will recognize the general shape of function (absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic) families and will convert between graphic and symbolic forms of functions. A transformational approach to graphing will be employed. Graphing calculators will be used as a tool to investigate the shapes and behaviors of these functions.
 Essential Knowledge and Skills Recognize graphs of parent functions. Given a transformation of a parent function, identify the graph of the transformed function. Given the equation and using a transformational approach, graph a function. Given the graph of a function, identify the parent function. Given the graph of a function, identify the transformations that map the preimage to the image in order to determine the equation of the image. Using a transformational approach, write the equation of a function given its graph. Essential Understandings The graphs/equations for a family of functions can be determined using a transformational approach. Transformations of graphs include translations, reflections, and dilations. A parent graph is an anchor graph from which other graphs are derived with transformations.
Vertical Articulation
1. SOL A.6 - graph linear equations/linear inequalities ( in 2 variables) ‐ a) determine slope of line given equation of line/ graph of line or two points on line ‐ slope as rate of change; b) write equation of line given graph of line, two points on line or slope & point on line.
2. SOL AFDA.2 - use transformations to write equations, given graph of function (linear/quad/exponential/log)
Instructional Materials
1. VDOE ESS Lesson: Transformational Graphing - Functions (PDF) - Exploring transformational graphing (Word)
2. Notes: Transformations (ppt)
Real World Lessons
Practice
Self-Assessments
Skills
1. Mathematics Assessment Project: A16:Sorting Functions - Apprentice - You are given four graphs, four equations, four tables, and four rules. Your task is to match each graph with an equation, a table and a rule.
2. JMU Pivotal Question: Transformational Graphing - Absolue Value (doc)
3. JMU Pivotal Question: Transformational Graphing - Exponential (doc)
Videos
Explore Learning
1. Cubic Function Activity - Explore a cubic function, along with the associated Center of Rotation. Vary the coefficients of the equation and examine how the graph changes in response.
2. Exponential Functions - Activity A - Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of the function.
3. Fourth-Degree Polynomials - Activity A - Compare the equation of a fourth‑degree polynomial to its graph. Vary the coefficients of the equation and investigate how the graph changes in response.
4. 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.
5. Functions Involving Square Roots - Compare the graph of a function involving square roots to its equation. Vary the coefficients of the equation and investigate how the graph changes in response.
6. General Form of a Rational Function - Compare the equation of a rational function to its graph. Multiply or divide the numerator and denominator by linear factors and explore how the graph changes in response.
7. Logarithmic Functions - Activity A - Compare the equation of a logarithmic function to its graph. Change the base of the logarithmic function and examine how the graph changes in response. Use the line y = x to compare the associated exponential function.
8. Radical Functions - Compare the graph of a radical function to its equation. Vary the terms of the equation. Explore how the graph is translated and stretched by the changes to the equation.
9. Rational Functions - Compare the graph of a rational function to its equation. Vary the terms of the equation and explore how the graph is translated and stretched as a result. Examine the domain on a number line and compare it to the graph of the equation.
Websites
Common Core Standards
 A-REI.4a A-REI.10 F-IF.7b F-IF.7d F-IF.7e F-IF.8b F-LE.1b F-LE.1c F-LE.2 F-LE.3 F-LE.4 F-LE.5