Transformations of 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, f(x + k) moves it left k, k·f(x) stretches it vertically, and f(kx) stretches it horizontally. Inside changes affect x; outside changes affect y.
Worked example
Compare g(x) = (x − 2)^2 + 3 to the parent f(x) = x^2. The (x − 2) shifts the graph right 2 units, and the + 3 shifts it up 3 units. So the vertex moves from (0, 0) to (2, 3).
Practice questions
- Describe how f(x) + 5 changes the graph of f(x) = x^2.
- How does f(x − 4) transform the parent function?
- Describe the effect of 3·f(x) on the graph of f(x) = x.
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
Transformaciones de Gráficas
Cambiar una función desplaza o estira su gráfica: f(x) + k la sube k, f(x + k) la mueve a la izquierda k, k·f(x) la estira verticalmente, y f(kx) la estira horizontalmente. Los cambios dentro afectan a x; los cambios fuera afectan a y.
Ejemplo: Compara g(x) = (x − 2)^2 + 3 con la función madre f(x) = x^2. El (x − 2) desplaza la gráfica 2 unidades a la derecha, y el + 3 la desplaza 3 unidades hacia arriba. Así que el vértice se mueve de (0, 0) a (2, 3).
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