Transformations of Function Graphs
Aligned to F-BF.B.3 — Common Core State Standards for Mathematics.
What this lesson teaches
Compared with f(x): f(x) + k shifts the graph up by k, f(x + k) shifts it left by k, k × f(x) stretches it vertically by a factor of k, and f(kx) compresses it horizontally. A negative k also reflects the graph.
Worked example
Start with f(x) = x^2. Then f(x) + 3 = x^2 + 3 shifts the parabola up 3 units, and f(x − 2) = (x − 2)^2 shifts it right 2 units.
Practice questions
- How does the graph of f(x) − 4 differ from the graph of f(x)?
- Describe the shift from f(x) to f(x + 5).
- Compare the graphs of f(x) = x^2 and 3 × f(x) = 3x^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.
▶ Watch this lessonEn español
Transformaciones de gráficas de funciones
Comparado con f(x): f(x) + k desplaza la gráfica k unidades hacia arriba, f(x + k) la desplaza k unidades a la izquierda, k × f(x) la estira verticalmente por un factor de k, y f(kx) la comprime horizontalmente. Un valor negativo de k también refleja la gráfica.
Ejemplo: Parte de f(x) = x^2. Entonces f(x) + 3 = x^2 + 3 desplaza la parábola 3 unidades hacia arriba, y f(x − 2) = (x − 2)^2 la desplaza 2 unidades a la derecha.
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