Functions, Graphs and Features

Lesson 4

Math

Unit 1

9th Grade

Lesson 4 of 11

Objective


Identify the domain and range through contextual situations, and explore domain and range on a graph. Represent domain and range with inequalities.

Common Core Standards


Core Standards

  • F.IF.A.1 — Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
  • F.IF.B.5 — Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. 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.

Foundational Standards

  • 8.F.A.1
  • 8.F.A.2

Criteria for Success


  1. Describe domain as the set of all possible inputs for the independent variable for a context and as the corresponding x-coordinates on the coordinate plane. 
  2. Describe the range as the set of all possible outputs for the dependent variable for a context and as the corresponding y-coordinates on the coordinate plane. 
  3. Identify the domain and range of a function presented algebraically, verbally, graphically, and in contexts. 

Tips for Teachers


  • This will not be the only lesson on domain and range. This concept will be revisited throughout the year, with various functions, but with particular focus on domain and range in Unit 5, with piecewise functions. 
  • This lesson uses inequalities to represent the domain and range of a function, but students will likely be unfamiliar with compound inequalities. The concept of a compound inequality can be introduced in this lesson, or the domain can be represented with two different inequalities. Either way works, but students will benefit from thinking about two separate inequalities in the graphical work in Anchor Problem #2. 
  • Ensure that students are using $$x$$ as the variable for the domain when writing inequalities and using $$y$$ as the variable for range when writing inequalities. 
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Anchor Problems


Problem 1

You are selling cookies for a fundraiser. You have a total of 25 boxes to sell, and you make a profit of $2 on each box. The profit you make $${p(n)}$$ is a function of the number of boxes you sell, $$n$$.

a.   Write an equation that represents this function, in function notation. 

b.   Describe the domain of this function. Then write an inequality to represent the domain.

c.   Describe the range of this function.

Guiding Questions

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Problem 2

Below is a graph of the linear function represented contextually above. Mark the domain on the graph, using vertical lines, and the range on the graph, using horizontal lines.

Guiding Questions

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Problem 3

What is the domain and range of this function?

Guiding Questions

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Problem Set


Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task


The Oakland Coliseum, home of the Oakland Raiders, is capable of seating 63,026 fans. For each game, the amount of money that the Raiders’ organization brings in as revenue is a function of the number of people, $$n$$, in attendance. If each ticket costs $30.00, find the domain and range of this function. Write the domain and range as inequalities. 

References

Illustrative Mathematics Oakland Coliseum

Oakland Coliseum, accessed on June 23, 2017, 9:21 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Additional Practice


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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Lesson 3

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Lesson 5

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Features of Functions

Topic B: Nonlinear Functions

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