Curriculum  /  Math  /  9th Grade  /  Unit 1: Functions, Graphs and Features  /  Lesson 3

Functions, Graphs and Features

Lesson 3

Math

Unit 1

9th Grade

Lesson 3 of 11

Objective

Identify features of functions, including x-intercept and y-intercept, in context. Evaluate function notation in context.

Common Core Standards

Core Standards

  • F.IF.A.2 — Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
  • F.IF.C.9 — Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.

Foundational Standards

  • 8.EE.B.5
  • 8.F.A.2
  • 8.F.B.4

Criteria for Success

  1. Describe that a function can be represented algebraically, verbally, graphically, or in a table of values. 
  2. Describe when a function is linear and whether the linear relationship is proportional. 
  3. Evaluate functions presented in function notation—either in equation or coordinate point form. 
  4. Describe how to find the y-intercept, x-intercept, and interval in a function presented algebraically, graphically, and in tabular form. 
  5. Interpret the intercepts of a contextual situation with and without function notation. 

Tips for Teachers

  • This lesson is the first one that uses function notation with an equation. The teacher will need to look out for misconceptions around this—specifically that the  is the same variable throughout and that the equation represents the rule that you use to get the outputs of the function.
  • This lesson connects strongly to middle school content throughout 6th, 7th, and 8th grade. Students are practicing translating between all forms of a linear function, with the added layer of using and interpreting function notation. 
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Anchor Problems

Problem 1

Do all of these representations describe the same function? How do you know? 

$${f(x)=2x}$$   
x y
-1 -2
0 0
1 2
2 4

 

 Each avocado costs $2. 

 

Guiding Questions

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Problem 2

Arianna is emptying a 175-gallon water tank. She knows that when she empties a similar style tank that is only 12.5 gallons, it takes 30 minutes.

What are the $$x$$ and $$y$$ intercepts? What do the intercepts represent in the context of the problem? 

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

Problem 1

Let $${f(t)}$$ be the value of a house, in thousands of dollars, after 2005. Explain the meaning of the following statements in context. Identify the $${x-}$$intercept and the $${y-}$$intercept.

$${f(0)=200}$$

$${f(3)=0}$$

Problem 2

Below is a situation presented graphically, algebraically, tabularly, and in word-problem form. Describe how you would find the $${x-}$$ and $${y-}$$intercepts in each of the representations. Describe the meaning of the intercepts in context of the problem.

$${f(x)=-3x+100}$$
$$x$$ $$y$$
5 85
10 70
15 55
20 40
You have $100 to spend on snacks. You decide that you will spend $3 a day. 

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.

  • Illustrative Mathematics, “The Aquarium”  can be adapted to include all of the criteria for success. Focus on the idea of intercepts and how these would be represented graphically, tabularly, and algebraically. Consider splitting this problem into multiple parts throughout the problem set.
  • Include problems presented as a graph, verbal description, and functions written algebraically, and ask students to consider the features of linearity, proportionality, and intercepts. 
  • Include problems that give the intercepts in function notation and a description of the variables. Describe the intercepts in context. 
  • Be sure to give a few problems written not in function notation but in standard form of a linear equation, and have students calculate and interpret the $$x$$ and $$y$$ intercepts graphically and contextually.
  • Include problems where students need to translate between all forms. 
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Lesson 2

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Lesson 4

Lesson Map

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

Topic A: Features of Functions

Topic B: Nonlinear Functions

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