AII.7d 
The student will investigate and analyze functions algebraically and graphically. Key concepts include
d) intervals in which a function is increasing or decreasing;
Graphing calculators will be used as a tool to assist in investigation of functions. 

Essential Knowledge and Skills 
 Given the graph of a function, identify intervals on which the function is increasing and decreasing.

Essential Understandings 
 Functions may be used to model realworld situations.
 A function can be described on an interval as increasing, decreasing, or constant.


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)
 Notes: Increasing and Decreasing Intervals (ppt)
 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: Increasing and Decreasing Intervals Practice (doc)
 Worksheet: Function Characteristics Review (doc)

SelfAssessments 
 SOL MiniQuiz: AII.7d  Increasing and Decreasing Intervals of Functions

Skills 
 JMU Pivotal Question: Analyzing Functions (doc)

Videos 

Explore
Learning 

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 
