AII.7c 
The student will investigate and analyze functions algebraically and graphically. Key concepts include
c) x and yintercepts;
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.

Essential Understandings 
 Functions may be used to model realworld situations.


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: Rational Functions: Intercepts, Asymptotes, and Discontinuity (PDF)  Exploring asymptotes and discontinuity (Word)
 Stations: Function Characteristic Card Sort (doc)

Real World Lessons 

Practice 
 7ce  VDOE ESS: Investigating Functions (pdf)
 Worksheet: Finding Intercepts Practice (doc)
 Worksheet: Function Characteristics Review (doc)

SelfAssessments 
 SOL MiniQuiz: AII.7c  x and yIntercepts of a Functions

Skills 
 Mathematics Assessment Project: A17:Cubic Graph  Apprentice  In this task, you will look at the properties of a cubic equation.
 JMU Pivotal Question: Intercepts (doc)

Videos 

Explore
Learning 
 Polynomials and Linear Factors  Create a polynomial as a product of linear factors. Vary the values in the linear factors to see how their connection to the roots of the function.
Using Tables, Rules and Graphs  Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change.

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 
