Lesson 3

Interpreting & Using Function Notation

Lesson Narrative

In this lesson, students continue to develop their ability to interpret statements in function notation in terms of a situation, including reasoning about inequalities such as \(f(a) > f(b)\). They now have to pay closer attention to the units in which the quantities are measured to effectively interpret symbolic statements. Along the way, students practice reasoning quantitatively and abstractly (MP2) and attending to precision (MP6).

Students also begin to connect statements in function notation to graphs of functions. They see each input-output pair of a function \(f\) as a point with coordinates \((x, f(x))\) when \(x\) is the input, and use information in function notation to sketch a possible graph of a function.

Students’ work with graphs is expected to be informal here. In a later lesson, students will focus on identifying features of graphs more formally.

Learning Goals

Teacher Facing

  • Describe connections between statements that use function notation and a graph of the function.
  • Practice interpreting statements that use function notation and explaining (orally and in writing) their meaning in terms of a situation.
  • Sketch a graph of a function given statements in function notation.

Student Facing

  • Let’s use function notation to talk about functions.

Learning Targets

Student Facing

  • I can describe the connections between a statement in function notation and the graph of the function.
  • I can use function notation to efficiently represent a relationship between two quantities in a situation.
  • I can use statements in function notation to sketch a graph of a function.

CCSS Standards


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