AII.7a 
The student will investigate and analyze functions algebraically and graphically. Key concepts include
a) domain and range, including limited and discontinuous domains and ranges;
Graphing calculators will be used as a tool to assist in investigation of functions. 

Essential Knowledge and Skills 
 Identify the domain, range, zeros, and intercepts of a function presented algebraically or graphically.
 Describe restricted/discontinuous domains and ranges.

Essential Understandings 
 Functions may be used to model realworld situations.
 The domain and range of a function may be restricted algebraically or by the realworld situation modeled by the function.


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: Functions: Domain, Range, End Behavior, Increasing or Decreasing (PDF)  Finding domain and range; determining whether a function is increasing or decreasing (Word)
 VDOE ESS Lesson: Rational Functions: Intercepts, Asymptotes, and Discontinuity (PDF)  Exploring asymptotes and discontinuity (Word)
 Notes: Domain and Range (ppt)
 Activity: Desmos  Exploring Domain and Range (doc)
 Stations: Function Characteristic Card Sort (doc)

Real World Lessons 

Practice 
 VDOE ESS: Where to Begin and End  Increasing, Decreasing, and End Behavior (pdf)
 VDOE ESS: Domain and Range (pdf)
 Worksheet: Domain and Range Practice (doc)
 Worksheet: Function Characteristics Review (doc)

SelfAssessments 
 SOL MiniQuiz: AII.7a  Domain and Range of Functions

Skills 

Videos 

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.

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 
