Curriculum / Math / 9th Grade / Unit 4: Linear Equations, Inequalities and Systems / Lesson 5
Math
Unit 4
9th Grade
Lesson 5 of 14
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Find inverse functions algebraically, and model inverse functions from contextual situations.
The core 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.
F.IF.B.6 — Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Modeling is best interpreted not as a collection of isolated topics but in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
The foundational standards covered in this lesson
8.F.A.1 — Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. Function notation is not required in Grade 8.
8.F.B.4 — Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
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
25-30 minutes
Below is a function and its inverse from the previous lesson.
Write the equations that model each of these functions. How do you calculate the inverse algebraically?
Find the algebraic inverse of the following function:
$${g(x)=3x -4}$$
A set of suggested resources or problem types that teachers can turn into a problem set
15-20 minutes
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
What is an equation of the line formed when the line $${y=3x+1}$$ is reflected in the line $${y=x}$$?
a. $${y=3x-1}$$
b. $${y=\frac{x-1}{3}}$$
c. $${y= \frac{x}{3}-1}$$
d. $${x=y}$$
F.BF.B.4: Inverse of Functions 1a is made available on JMAP by Steve Sibol and Steve Watson. Copyright © 2017 JMAP, Inc. - All rights reserved. Accessed Oct. 19, 2017, 2:52 p.m..
What is the inverse of the function $${y=2x+3}$$?
a. $${x=\frac{1}{2}y-\frac{3}{2}}$$
b. $${x=\frac{1}{2}x-\frac{3}{2}}$$
c. $${y=2x-3}$$
d. $${x=-2y-3}$$
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.
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Describe the solutions and features of a linear inequality. Graph linear inequalities.
Topic A: Properties and Solutions of Two-Variable Linear Equations and Inverse Functions
Identify the solutions and features of a linear equation and when two linear equations have the same solutions.
Standards
A.REI.D.10A.SSE.B.3
Write linear equations given features, points, or graph in standard form, point-slope form, and slope-intercept form.
A.SSE.B.3F.IF.B.4F.IF.C.7.A
Determine if a function is linear based on the rate of change of points in the function presented graphically and in a table of values.
F.IF.B.6F.IF.C.7.AF.IF.C.9F.LE.A.1.A
Identify inverse functions graphically and from a table of values in contextual and non-contextual situations.
F.BF.B.4.AF.IF.A.1F.IF.A.2F.IF.B.5
A.CED.A.4F.BF.B.4.AF.IF.B.6
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Topic B: Properties and Solutions of Two-Variable Linear Inequalities
A.REI.D.12
Write linear inequalities from graphs.
A.CED.A.3A.REI.D.12
Write linear inequalities from contextual situations.
A.CED.A.3
Topic C: Systems of Equations and Inequalities
Solve a system of linear equations graphically.
A.CED.A.3A.REI.D.11
Identify solutions to systems of inequalities graphically. Write systems of inequalities from graphs and word problems.
Solve linear systems of equations of two variables by substitution.
A.CED.A.3A.REI.C.5A.REI.C.6N.Q.A.2
Identify solutions to systems of equations algebraically using elimination. Write systems of equations.
A.REI.C.5
Identify solutions to systems of equations using any method. Write systems of equations.
A.REI.A.1A.REI.C.6A.SSE.B.3
Identify solutions to systems of equations with three variables.
A.REI.C.6
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