Expressions and Operations 

Equations and Inequalities 

Functions 

Statistics 

SOL Review Materials 




A.7abf 
The student will investigate and analyze function (linear and quadratic) families and their characteristics both algebraically and graphically, including
a) determining whether a relation is a function;
b) domain and range; and
f) making connections between and among multiple representations of functions including concrete, verbal, numeric, graphic, and algebraic. 

Essential Knowledge and Skills 
 Determine whether a relation, represented by a set of ordered pairs, a table, or a graph is a function.
 Identify the domain, range, zeros, and intercepts of a function presented algebraically or graphically.
 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 
 A set of data may be characterized by patterns, and those patterns can be represented in multiple ways.
 Graphs can be used as visual representations to investigate relationships between quantitative data.
 Inductive reasoning may be used to make conjectures about characteristics of function families.
 Each element in the domain of a relation is the abscissa of a point of the graph of the relation.
 Each element in the range of a relation is the ordinate of a point of the graph of the relation.
 A relation is a function if and only if each element in the domain is paired with a unique element of the range.
 The values of f(x) are the ordinates of the points of the graph 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)
 Notes: Functions and Relations (doc)  Answer Key (pdf)
 Notes: Domain and Range (flipchart)

Real World Lessons 

Practice 
 VDOE ESS: Building Square Patios (pdf)
 Worksheet: Relations CW (doc)
 Worksheet: Relations HW (doc)
 ExamView Quiz: Relations

SelfAssessments 
 SOL Mini Quiz

Skills 
 JMU Pivotal Question:Domain and Range Scenarios (doc)
 JMU Pivotal Question:Domain of Functions (doc)
 JMU Pivotal Question: Range of Functions (doc)

Videos 
 Video: PH Identifying Functions using a Mapping
 Video: PH Identifying Functions using a Vertical Line Test
 Video: PH Determining a Reasonable Domain and Range for a Situation
 Video: PH Modeling a Function Using Three View

Explore
Learning 
 Introduction to Functions  Determine if a relation is a function using the mapping diagram, ordered pairs, or the graph of the relation. Drag arrows from the domain to the range, type in ordered pairs, or drag points to the graph to add inputs and outputs to the relation.
 Linear Functions  Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear.

Websites 
 Notes: Domain and Range  notes and interactives from Purplemath.com
 Notes: Functions  notes on functions, function boxes, domain and range, and mappings at Coolmath.com

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 

