Comparing Functions
Aligned to F-IF.C.9 — Common Core State Standards for Mathematics.
What this lesson teaches
To compare functions given in different forms (equation, table, or graph), find a common feature such as slope, rate of change, or maximum, then compare those values.
Worked examples
Example 1
Function A is y = 3x + 1. Function B is a table with (0, 2), (1, 6), (2, 10). B's rate of change is (6 − 2) / 1 = 4. Since 4 > 3, function B grows faster.
Example 2
Compare a linear and an exponential: y = 100x starts far ahead of y = 2^x and is overtaken before x = 15.
Example 3
Compare like with like. Reading slope from a graph and rate from a table is fine, but the axes must use the same units.
Practice questions
- Line A has slope 5; line B is y = 4x + 2. Which is steeper?
- One job pays $6 per hour; another is y = 8x. Which earns faster?
- Compare the y-intercepts of y = 2x + 7 and a table with (0, 3), (1, 5).
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
Comparar Funciones
Para comparar funciones dadas en distintas formas (ecuación, tabla o gráfica), halla una característica común como la pendiente, la tasa de cambio o el máximo, y luego compara esos valores.
Ejemplo 1: La función A es y = 3x + 1. La función B es una tabla con (0, 2), (1, 6), (2, 10). La tasa de cambio de B es (6 − 2) / 1 = 4. Como 4 > 3, la función B crece más rápido.
Ejemplo 2: Compara una lineal y una exponencial: y = 100x empieza muy por delante de y = 2^x y es rebasada antes de x = 15.
Ejemplo 3: Compara lo comparable. Leer la pendiente de una gráfica y la tasa de una tabla está bien, pero los ejes deben usar las mismas unidades.
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