Expressions and Operations 

Equations and Inequalities 

Functions 

Statistics 

SOL Review Materials 




A.7e 
The student will investigate and analyze function (linear and quadratic) families and their characteristics both algebraically and graphically, including
e) finding the values of a function for elements in its domain. 

Essential Knowledge and Skills 
 For each x in the domain of f, find f(x).
 Represent relations and functions using concrete, verbal, numeric, graphic, and algebraic forms. Given one representation, students will be able to represent the relation in another form.
 Detect patterns in data and represent arithmetic and geometric patterns algebraically.

Essential Understandings 
 The values of f(x) are the ordinates of the points of the graph of f.
 The object f(x) is the unique object in the range of the function f that is associated with the object x in the domain of f.
 For each x in the domain of f, x is a member of the input of the function f, f(x) is a member of the output of f, and the ordered pair [x, f(x)] is a member of f.
 Set builder notation may be used to represent domain and range of a relation.


Vertical Articulation 
 SOL 7.12  represent relationships with tables, graphs, rules, and words
 SOL 8.14  make connections between any two representations (tables, graphs, words, rules)
 SOL 8.17  identify domain, range, independent/dependent variable
 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)
 SOL AII.7  investigate/analyze functions (algebraically/ graphically) a) domain/range; b) zeros; c) x‐ and y‐intercepts; d) intervals of increasing/decreasing; e) asymptotes; f) end behavior; g) inverse of a function; h) composition of multiple functions

Instructional Materials 
 VDOE ESS Lesson: Square Patios  Functions (PDF)  Connecting different representations of functions (Word)
 VDOE ESS Lesson: Functions 1  Functions (PDF)  Investigating relations and functions (Word)
 VDOE ESS Lesson: Functions 2  Functions (PDF)  Investigating domain, range, intercepts, and zeros (Word)
 Notes: Finding Function Values (doc)  Answer Key (pdf)
 Guided Notes: Function Notation and Evaluating Functions (doc)
 Activity: Functions Fair/Not Fair (doc)

Real World Lessons 

Practice 
 VDOE ESS: Building Square Patios (pdf)
 VDOE ESS: Exploring Functions (pdf)
 Worksheet: Finding Function Values CW (doc)
 Worksheet: Finding Function Values HW (doc)
 Project Graduation Quotable Puzzle (doc)  (pdf)
 ExamView Quiz: Functions
 Prentice Hall Quiz
 Functions Review Flipchart

SelfAssessments 
 SOL Mini Quiz

Skills 
 JMU PIvotal Question: Finding Function Values (doc)
 JMU PIvotal Question: Finding Parabola Values (doc)

Videos 
 Video: PH Making a Table from a Function Rule
 Video: PH Finding the Range of a Function Given the Domain

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 
 Interactive: Function Machine  investigate simple linear functions by trying to guess the algebraic form from inputs and outputs at Shodor.org.
 Interactive: Function Machine  investigate simple linear functions by trying to guess the algebraic form from inputs and outputs at Shodor.org.
 Interactive: Vertical Line Test  discovery activity that determines if a graph is a function at Shodor.org.
 Interactive: Graphs and Functions view images of graphs at Shodor.org and determine if they represent a function

Old Website Links 

Common Core
Standards 
8.F.3 
8.F.4 
8.F.5 
AAPR.3 
FIF.1 
FIF.2 
FIF.4 
FIF.5 
FIF.7a 
FIF.7c 
FIF.9 
FBF.1a 
FBF.1b 
FBF.3 
FLE.2 
FLE.5 

