Interpreting Function Parameters
Aligned to F-LE.B.5 — Common Core State Standards for Mathematics.
What this lesson teaches
In a model, each number has a real meaning — in y = mx + b, m is the rate of change and b is the starting value; in an exponential a·b^x, a is the start and b is the growth factor.
Worked examples
Example 1
A gym cost is C(x) = 5x + 20. The 5 means each visit costs $5 (the rate), and the 20 is the $20 one-time join fee (the starting value).
Example 2
In A = 5000(1.03)^t, the 5000 is the starting amount and the 1.03 is a 3% growth rate — the parameter is the rate plus one.
Example 3
If a parameter has no meaning in the story, the model is wrong for the story. A negative join fee should stop you.
Practice questions
- In y = 3x + 50, what do the 3 and the 50 mean if y is total pay?
- In P(x) = 200 × 1.5^x, what does the 200 represent?
- In P(x) = 200 × 1.5^x, what does the 1.5 tell you about growth?
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.
▶ Watch this lessonEn español
Interpretar los Parámetros de una Función
En un modelo, cada número tiene un significado real: en y = mx + b, m es la tasa de cambio y b es el valor inicial; en una exponencial a·b^x, a es el inicio y b es el factor de crecimiento.
Ejemplo 1: El costo de un gimnasio es C(x) = 5x + 20. El 5 significa que cada visita cuesta $5 (la tasa), y el 20 es la cuota única de inscripción de $20 (el valor inicial).
Ejemplo 2: En A = 5000(1.03)^t, el 5000 es la cantidad inicial y el 1.03 es una tasa de crecimiento del 3% — el parámetro es la tasa más uno.
Ejemplo 3: Si un parámetro no significa nada en el enunciado, el modelo está mal para ese enunciado. Una cuota de inscripción negativa debe detenerte.
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