2016-2017 Curriculum Blueprint
Grade: 9-12
Course: Algebra 2 Honors
4 days
Module 8: Rational Functions
Learning Goal
The student is expected to graph rational
functions, identifying asymptotes, end
behavior, and also describe and explain the
key features of the graph of a complicated
rational function.
Essential Questions
Unit Overview
1
1. How the graphs of (𝑓(𝑥) = 𝑎 (𝑥−ℎ) + 𝑘 𝑎𝑛𝑑 𝑓(𝑥) =
(1
1
(𝑥−ℎ)
1
) + 𝑘 are related to the graph of𝑓(𝑥) = ?
𝑥
𝑏
Approximate Time:
This unit focuses on graphing rational functions, adding and
subtracting rational expressions, multiplying and dividing rational
expressions, graphing and solving rational equations
2. What features of the graph of a rational function
should you identify in order to sketch the graph? How
do you identify those features?
Vertical Progression:
MAFS.912.A-APR.2.3, A-REI.4.11, F-BF.2.3, F-BF.3.7b, c, e: In Algebra 1, students’ would have explored with factoring, finding the zeros, graphing polynomials by identifying key
features of polynomial functions which includes but not limited to domain, range, intercepts, end behavior, transformations, and degree.
Module Focus Standards
Module Topics
Essential Vocabulary
Algebra 2 Item Specs (FSA Reference Sheet located at the end of Item Specs)
High School Flip Book
MAFS.912.A-APR.4.6: (DOK2) Rewrite simple rational expressions in different
forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x)
are polynomials with the degree of r(x) less than the degree of b(x), using
inspection, long division, or, for the more complicated examples, a computer
algebra system.
 Use inspection to rewrite simple rational expressions in different forms; write
a(x)/ b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are
polynomials with the degree of r(x) less than the degree of b(x).
 Use long division to rewrite simple rational expressions in different forms;
write a(x)/ b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are
polynomials with the degree of r(x) less than the degree of b(x).
 Use a computer algebra system to rewrite complicated rational expressions in
different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x),
q(x), and r(x) are polynomials with the degree of r(x) less than the degree of
b(x).
Graphing Simple Rational Functions (FIF.3.7d(+), A-APR.4.6, F-BF.2.3)
Core Resource:
 Lesson 8.1- (HMH Book)




MAFS.912.A-SSE.1.1b: (DOK2) Interpret expressions that represent a quantity in
terms of its context. (b) Interpret complicated expressions by viewing one or
more of their parts as a single entity. For example, interpret as the product of P
and a factor not depending on P.
 Interpret complicated expressions, in terms of the context, by viewing one or
more of their parts as a single entity.
Additional Resource:
 Pre-calculus: Module 3 Lesson 14 – Engage NY
 Transformations and Simple Rational
Functions - Geogebra
 Graphing Worksheet - Alaska
Formative Assessments:
 Graphing a Rational Function - CPALMS
 Lesson Performance Task (HMH pg. 400)
Graphing More Complicated Rational
Functions (F-IF.3.7d(+), A-SSE.1.1b,A-APR.4.6)
Core Resource:
 Lesson 8.2: (HMH Book)
NOTE: Explore 1 Part A&B only, Explain 1 and
Example 1 only
Additional Resource:
 Pre-calculus Module 3 Lesson 14 – Engage NY
 Rational Functions - Utah
Asymptote
Constant of variation
Parent function
Rational function
Higher Order Question Stems
 How would a diagram, graph, table… help?
 What mathematical consistencies do you
notice?
Writing Connections
 Write to explain your visual representation
 Write to explain the short cut and justify why
it works.
Link to Webb’s DOK Guide
2016-2017 Curriculum Blueprint
Grade: 9-12
Course: Algebra 2 Honors
Module 8: Rational Functions
MAFS.912.F-BF.2.3: (DOK2) Identify the effect on the graph of replacing f(x) by
f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and
negative); find the value of k given the graphs. Experiment with cases and
illustrate an explanation of the effects on the graph using technology. Include
recognizing even and odd functions from their graphs and algebraic expressions
for them.
 Given a single transformation on a symbolic or graphic function, identify the
effect on the graph.
 Using technology, identify effects of single transformations on graphs of
functions.
 Graph a given function by replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for
specific values of k (both positive and negative).
 Describe the differences and similarities between a parent function and the
transformed function.
 Find the value of k, given the graphs of a parent function, f(x), and the
transformed function: f(x) + k, k f(x), f(kx), or f(x + k).
 Recognize even and odd functions from their graphs and equations.
 Experiment with cases and illustrate an explanation of the effects on the
graph, using technology.
MAFS.912.F-IF.3.7d: (+) (DOK2) Graph functions expressed symbolically and show
key features of the graph, by hand in simple cases and using technology for more
complicated cases. (d) Graph rational functions, identifying zeros and asymptotes
when suitable factorizations are available, and showing end behavior.
 Graph rational functions, by hand in simple cases or using technology for
more complicated cases, and show/label the graph, identify zeros when
suitable factorizations are available, and show end behavior.
Mathematical Practice Standards
Link to Mathematical Practice Standards Rubric
MAFS.K12.MP.4.1:Model with Mathematics
MAFS.K12.MP.8.1: Look for and express regularity in repeated reasoning.
 Rational Functions 2 – Richland, IL
 Intercepts, Asymptotes, Discontinuity Virginia
 Rational Functions Worksheet pg. 13-24 Georgia
 Graphing Worksheet
Formative Assessments:
 Graphing Rational Functions – Illustrative
Math
 Lesson Performance Task (HMH pg. 418)
Approximate Time:
4 days