CurriculumGrade 12Mathematics

Comparing Functions in Different Forms

Aligned to F-IF.C.9 — Common Core State Standards for Mathematics.

What this lesson teaches

To compare two functions given in different ways — equation, table, graph, or words — pick a shared feature such as rate of change, intercept, or maximum, and read that feature from each representation.

Worked example

Function A is f(x) = 3x + 2 (an equation, slope 3). Function B is a table passing through (0, 1) and (1, 5), so its slope is (5 − 1)/(1 − 0) = 4. Since 4 > 3, Function B grows faster.

Practice questions

  1. Function A has slope 2; a table for B rises 5 units per step. Which grows faster?
  2. Compare the y-intercepts of f(x) = 2x − 3 and a line through (0, 4).
  3. A parabola f(x) = x^2 − 4 has minimum −4; a graphed parabola has minimum −1. Which minimum is greater?

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

Comparar funciones en distintas formas

Para comparar dos funciones dadas de distinta manera — ecuación, tabla, gráfica o en palabras — elige una característica común como la tasa de cambio, la intersección o el máximo, y léela en cada representación.

Ejemplo: La función A es f(x) = 3x + 2 (una ecuación, pendiente 3). La función B es una tabla que pasa por (0, 1) y (1, 5), así que su pendiente es (5 − 1)/(1 − 0) = 4. Como 4 > 3, la función B crece más rápido.

More Functions lessons

Trigonometric Functions and the Unit CircleF-TF.A.2Equivalent Forms of a FunctionF-IF.C.8Building Functions from Two QuantitiesF-BF.A.1Transformations of Function GraphsF-BF.B.3Inverse FunctionsF-BF.B.4Radian Measure and Arc LengthF-TF.A.1

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