Using Function Notation to Describe Rules (Part 1)

5 min

Narrative

This Warm-up familiarizes students with a new way of using function notation and gives them a preview of the work in this lesson.

The prompt also gives students opportunities to see and make use of structure (MP7). The specific structure they might notice is how the values in the f(x)f(x) and the g(x)g(x) columns in each table correspond to the expression describing each function.

When students articulate what they notice and wonder, they have an opportunity to attend to precision in the language they use to describe what they see (MP6). They might first use less formal or imprecise language and then restate their observation with more precise language in order to communicate more clearly.

Launch

Arrange students in groups of 2. Display the two tables for all to see. Ask students to think of at least one thing they notice and at least one thing they wonder. Give students 1 minute of quiet think time, and then 1 minute to discuss with their partner the things they notice and wonder.

Student Task

What do you notice? What do you wonder?

xx f(x)=10−2xf(x)=10-2x
1 8
1.5 7
5 0
-2 14
xx g(x)=x3g(x)=x^3
-2 -8
0 0
1 1
3 27

Sample Response

Students may notice:

  • The tables don’t say “input” and “output” or “xx” and “yy.”
  • One function is called ff. The other is called gg.
  • There’s an expression (rather than a number) on the right side of the equations f(x)=10−2xf(x)=10-2x and g(x)=x3g(x)=x^3.
  • If we substitute the values in the left column for the xx in the expression, we get the values in the right column.

Students may wonder:

  • Why is there now xx on the right side of the equal sign?
  • Are there rules about how to name functions?
  • What does each equation (f(x)=10−2xf(x)=10-2x and g(x)=x3g(x)=x^3) mean?
Activity Synthesis (Teacher Notes)

Ask students to share the things they noticed and wondered. Record and display their responses without editing or commentary for all to see. If possible, record the relevant reasoning on or near the tables. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and respectfully ask for clarification, point out contradicting information, or voice any disagreement.

Standards
Addressing
  • F-IF.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.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.2·Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
  • HSF-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.
Building Toward
  • F-BF.1·Write a function that describes a relationship between two quantities
  • F-BF.1·Write a function that describes a relationship between two quantities
  • F-BF.1·Write a function that describes a relationship between two quantities
  • F-BF.1·Write a function that describes a relationship between two quantities
  • F-BF.1·Write a function that describes a relationship between two quantities
  • F-BF.1·Write a function that describes a relationship between two quantities
  • HSF-BF.A.1·Write a function that describes a relationship between two quantities.

10 min

20 min