Average Rate of Change
Aligned to F-IF.B.6 — Common Core State Standards for Mathematics.
What this lesson teaches
The average rate of change of a function over an interval [a, b] is the change in output divided by the change in input: (f(b) − f(a)) / (b − a). It measures how fast the quantity changes on average.
Worked example
For f(x) = x^2, find the average rate of change from x = 1 to x = 4. Compute (f(4) − f(1)) / (4 − 1) = (16 − 1) / 3 = 15 / 3 = 5.
Practice questions
- Find the average rate of change of f(x) = 3x + 2 from x = 0 to x = 5.
- A table shows f(2) = 7 and f(6) = 19. Find the average rate of change.
- For f(x) = x^2, find the average rate of change from x = 2 to x = 3.
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
Tasa Promedio de Cambio
La tasa promedio de cambio de una función en un intervalo [a, b] es el cambio en la salida dividido entre el cambio en la entrada: (f(b) − f(a)) / (b − a). Mide qué tan rápido cambia la cantidad en promedio.
Ejemplo: Para f(x) = x^2, halla la tasa promedio de cambio de x = 1 a x = 4. Calcula (f(4) − f(1)) / (4 − 1) = (16 − 1) / 3 = 15 / 3 = 5.
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