CurriculumGrade 9Mathematics

What Is a Function?

Aligned to F-IF.A.1 — Common Core State Standards for Mathematics.

What this lesson teaches

A function assigns to each input exactly one output. Function notation f(x) names the output for input x, and the graph is the set of all ordered pairs (x, f(x)).

Worked example

Does {(1, 2), (3, 4), (1, 5)} define a function? The input 1 is paired with both 2 and 5, so no — an input cannot have two different outputs.

Practice questions

  1. Does {(0, 1), (2, 3), (4, 5)} define a function? Explain.
  2. If f(x) = x + 6, what ordered pair matches input x = 2?
  3. Explain why a vertical line can cross a function's graph at most once.

Watch the lesson

Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.

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En español

¿Qué Es una Función?

Una función asigna a cada entrada exactamente una salida. La notación de función f(x) nombra la salida para la entrada x, y la gráfica es el conjunto de todos los pares ordenados (x, f(x)).

Ejemplo: ¿{(1, 2), (3, 4), (1, 5)} define una función? La entrada 1 está emparejada con 2 y con 5, así que no: una entrada no puede tener dos salidas distintas.

More Functions lessons

Interpreting Graphs of FunctionsF-IF.B.4Evaluating FunctionsF-IF.A.2Sequences as FunctionsF-IF.A.3Domain in ContextF-IF.B.5Average Rate of ChangeF-IF.B.6Graphing Key FeaturesF-IF.C.7

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