Building Functions from Relationships
Aligned to F-BF.A.1 — Common Core State Standards for Mathematics.
What this lesson teaches
Write a function by expressing one quantity in terms of another using the words of the problem. Often you combine simpler function types, such as multiplying two linear expressions to get a quadratic.
Worked example
A rectangle's length is 3 more than its width w. Write its area as a function. Length is w + 3, so area A(w) = w(w + 3) = w^2 + 3w. This combines the width and length into one quadratic function.
Practice questions
- A number's square plus twice itself: write f(x) for this.
- A square has side s; write its perimeter and area as functions of s.
- A store's revenue is price p times quantity (100 − p): write R(p).
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Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Construir Funciones a partir de Relaciones
Escribe una función expresando una cantidad en términos de otra usando las palabras del problema. A menudo combinas tipos de funciones más simples, como multiplicar dos expresiones lineales para obtener una cuadrática.
Ejemplo: El largo de un rectángulo es 3 más que su ancho w. Escribe su área como función. El largo es w + 3, así que el área A(w) = w(w + 3) = w^2 + 3w. Esto combina el ancho y el largo en una sola función cuadrática.
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