Domain and Range (Part 2)

5 min

Narrative

This Warm-up prompts students to compare four unlabeled graphs. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology and talk about characteristics of the items in comparison to one another.

Students need to look for and make use of the structure of the graphs to determine how each one is like or unlike the others (MP7).

Student Task

Which three go together? Why do they go together?

A

<p>A graph with origin O. The graph is a line crossing the vertical axis and slants downward to cross the horizontal axis.</p>

B

<p>A graph. </p>
A graph with origin O. The graph is a step function with 6 horizontal line segments beginning with a closed circle and ending with an open circle. The next horizontal line begins where the previous line ends.

C

<p>A graph with origin O. The graph is a horizontal line passing through the middle of the vertical axis.</p>

D

<p>A graph.</p>
A graph with origin O. The graph increases and decreases quickly and is shaped like a wave. The height of the waves are larger in the middle than on the ends.

Sample Response

Sample response:

  • A, B, and C go together because they are made of lines.
  • A, B, and D go together because they have more than 1 output value.
  • A, C, and D go together because they are continuous (or connected).
  • B, C, and D go together because each output value has many corresponding input values.
Activity Synthesis (Teacher Notes)

Invite each group to share one reason why a particular set of three goes together. Record and display the responses for all to see. After each response, ask the class if they agree or disagree. Since there is no single correct answer to the question of which three go together, attend to students’ explanations and ensure the reasons given are correct.

During the discussion, ask students to explain the meaning of any terminology they use, such as “intercepts,” “minimum,” or “linear functions.” Also, press students on unsubstantiated claims.

Standards
Building On
  • F-IF.4·For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
  • F-IF.4·For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
  • F-IF.4·For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
  • F-IF.4·For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
  • F-IF.4·For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
  • F-IF.4·For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
  • HSF-IF.B.4·For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. <span>Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.</span>

20 min

10 min