Comparing Functions
Aligned to 8.F.A.2 — Common Core State Standards for Mathematics.
What this lesson teaches
Functions can be shown as equations, graphs, tables, or words. To compare them, find each function's rate of change (slope) and initial value (y-intercept) in the same form, then compare those numbers.
Worked examples
Example 1
Function A: y = 4x + 5. Function B is a table with (0, 3), (1, 6), (2, 9), so its slope is 3 and its intercept is 3. Comparing: A has the greater rate of change (4 > 3), while B has the smaller starting value (3 < 5).
Example 2
Plan A: $50 up front, $10/month (y = 10x + 50). Plan B: $20 up front, $15/month (y = 15x + 20). B is cheaper early, A is cheaper after month 6.
Example 3
Compare slopes for rate and intercepts for starting value — a function can win on one and lose on the other.
Practice questions
- Function A: y = 2x + 1. Function B passes through (0, 4) and (2, 10). Which has the greater slope?
- Which function above has the greater y-intercept?
- One savings plan starts at $20 and grows $5/week; another is y = 8x + 10. Which saves faster?
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
Comparación de Funciones
Las funciones pueden mostrarse como ecuaciones, gráficas, tablas o palabras. Para compararlas, halla la tasa de cambio (pendiente) y el valor inicial (intersección con el eje y) de cada una en la misma forma, y luego compara esos números.
Ejemplo 1: Función A: y = 4x + 5. La función B es una tabla con (0, 3), (1, 6), (2, 9), así que su pendiente es 3 y su intersección es 3. Comparando: A tiene mayor tasa de cambio (4 > 3), mientras que B tiene menor valor inicial (3 < 5).
Ejemplo 2: Plan A: $50 de entrada, $10/mes (y = 10x + 50). Plan B: $20 de entrada, $15/mes (y = 15x + 20). B es más barato al principio, A lo es después del mes 6.
Ejemplo 3: Compara pendientes para la tasa e intersecciones para el valor inicial — una función puede ganar en una y perder en la otra.
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