CurriculumGrade 12Mathematics

Building Functions from Two Quantities

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

What this lesson teaches

Model a relationship by combining simpler functions — adding, multiplying, or composing them — so that one quantity depends on another in a single expression.

Worked example

A store charges a $5 flat fee plus $2 per item, and then adds 10% tax. The total cost is C(n) = 1.10 × (5 + 2n). For n = 3 items, C(3) = 1.10 × (5 + 6) = 1.10 × 11 = $12.10.

Practice questions

  1. Write a cost function for a $20 base fee plus $3 per hour.
  2. A square has side length s = t + 1. Write its area as a function of t.
  3. A phone plan is $30 plus $0.10 per minute, then an 8% tax. Write the total-cost function.

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

Construir funciones a partir de dos cantidades

Modela una relación combinando funciones más simples — sumándolas, multiplicándolas o componiéndolas — para que una cantidad dependa de otra en una sola expresión.

Ejemplo: Una tienda cobra una tarifa fija de $5 más $2 por artículo, y luego agrega 10% de impuesto. El costo total es C(n) = 1.10 × (5 + 2n). Para n = 3 artículos, C(3) = 1.10 × (5 + 6) = 1.10 × 11 = $12.10.

More Functions lessons

Trigonometric Functions and the Unit CircleF-TF.A.2Equivalent Forms of a FunctionF-IF.C.8Comparing Functions in Different FormsF-IF.C.9Transformations of Function GraphsF-BF.B.3Inverse FunctionsF-BF.B.4Radian Measure and Arc LengthF-TF.A.1

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