Curriculum / Math / 11th Grade / Unit 4: Rational and Radical Functions / Lesson 3
Math
Unit 4
11th Grade
Lesson 3 of 18
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Graph and transform square root and cubic root 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.B — Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
The foundational standards covered in this lesson
F.BF.B.4.A — Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2 x3 or f(x) = (x+1)/(x—1) for x ? 1.
A.CED.A.4 — Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Below is a graph of a square root function.
What is the equation that represents this function?
Graph the following function on a coordinate plane:
$${f(x)={\sqrt{x-2}}+1}$$
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
How would the graph of $$f(x)=\sqrt{x}$$ be affected if it were changed to $$g(x)=-2\sqrt{x}$$?
Algebra I > Module 4 > Topic C > Lesson 20 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..
Sketch and label the graphs of both $$f$$ and $$g$$.
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 2
Lesson 4
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
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.
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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.
Describe transformations of rational functions.
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
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