Curriculum / Math / 11th Grade / Unit 4: Rational and Radical Functions / Lesson 13
Math
Unit 4
11th Grade
Lesson 13 of 18
Jump To
Describe transformations of rational functions.
The core standards covered in this lesson
F.BF.B.3 — 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.
F.IF.C.7.D — Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
The foundational standards covered in this lesson
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.
Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Given the graph shown below of $${a+{b\over(x+c)}}$$, where $${b=1}$$, $${c=0}$$, and $${a=0 }$$
Use this Desmos graph to describe the effect that changing the values of $$a$$, $$b$$, and $$c$$ has on the location of the graph.
Graph the function $${g(x)={x+2\over{{x-}3}}}$$ using asymptote(s), $${x-}$$ and $${y-}$$intercepts, and a sign chart.
What transformations have occurred from the parent function of $${1\over{x}}$$?
Precalculus and Advanced Topics > Module 3 > Topic B > Lesson 15 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Below is an equation and the graph of the function $${g(x)}$$.
$${g(x)}={3x-7\over{x-3}}$$
Describe the transformations that have occurred from the parent function of $${1\over{x}}$$. Write the equation of the rational function in the transformational form.
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
Lesson 12
Lesson 14
Topic A: Introduction to Rational and Radical Functions and Expressions
Define rational functions. Identify domain restrictions of rational functions.
A.APR.D.6 F.IF.B.5
Identify domain restrictions algebraically for non-invertible functions.
F.BF.B.4 F.IF.C.7.B
Graph and transform square root and cubic root functions.
F.BF.B.3 F.IF.C.7.B
Write rational functions in equivalent radical form and identify domain restrictions of rational and radical functions.
F.IF.B.5 N.RN.A.2
Write radical and rational exponent expressions in equivalent forms.
N.RN.A.2
Multiply and divide rational expressions and simplify using equivalent expressions.
A.APR.D.6 A.APR.D.7
Add and subtract rational expressions.
Create a free account to access thousands of lesson plans.
Already have an account? Sign In
Topic B: Features of Rational Functions and Graphing Rational Functions
Identify asymptotic discontinuities (also known as infinite discontinuities) and removable discontinuities in a rational function and describe why these discontinuities exist.
A.APR.D.6 F.IF.C.7.D
Identify features of rational functions with equal degrees in the numerator and the denominator. Describe how to calculate features of these types of rational functions algebraically.
Identify features of rational functions with a larger degree in the denominator than in the numerator. Describe how to calculate these features algebraically.
Identify features of rational functions with a larger degree in the numerator than in the denominator. Describe how to calculate these features algebraically.
Analyze the graph and equations of rational functions and identify features. Use features of a rational function to identify and construct appropriate equations and graphs.
F.BF.B.3 F.IF.C.7.D
Topic C: Solve Rational and Radical Equations and Model with Rational Functions
Solve simple radical equations.
A.REI.A.2
Solve radical equations and identify extraneous solutions.
Solve rational equations.
A.APR.D.6 A.REI.A.2 A.REI.D.11
Write and solve rational functions for contextual situations.
A.APR.D.6 A.CED.A.2 N.Q.A.1
Analyze rational and radical functions in context and write rational functions for percent applications.
A.APR.D.6 A.CED.A.2 A.REI.A.2
See all of the features of Fishtank in action and begin the conversation about adoption.
Learn more about Fishtank Learning School Adoption.
Yes
No
Access rigorous, relevant, and adaptable math lesson plans for free