CurriculumGrade 9Mathematics

Transforming Graphs

Aligned to F-BF.B.3 — Common Core State Standards for Mathematics.

What this lesson teaches

Changing a function shifts or stretches its graph: f(x) + k moves it up k units, f(x + k) moves it left k units, k·f(x) stretches it vertically, and a negative sign reflects it.

Worked example

How does y = x^2 + 3 compare to y = x^2? Adding 3 moves every point up 3 units, so the vertex shifts from (0, 0) to (0, 3).

Practice questions

  1. How does y = x^2 − 5 compare to y = x^2?
  2. Describe the shift from y = x^2 to y = (x + 2)^2.
  3. What does the negative sign do to the graph of y = −x^2?

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

Transformar Gráficas

Cambiar una función desplaza o estira su gráfica: f(x) + k la sube k unidades, f(x + k) la mueve k unidades a la izquierda, k·f(x) la estira verticalmente, y un signo negativo la refleja.

Ejemplo: ¿Cómo se compara y = x^2 + 3 con y = x^2? Sumar 3 mueve cada punto 3 unidades hacia arriba, así que el vértice pasa de (0, 0) a (0, 3).

More Functions lessons

Interpreting Graphs of FunctionsF-IF.B.4What Is a Function?F-IF.A.1Evaluating FunctionsF-IF.A.2Sequences as FunctionsF-IF.A.3Domain in ContextF-IF.B.5Average Rate of ChangeF-IF.B.6

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