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
- How does y = x^2 − 5 compare to y = x^2?
- Describe the shift from y = x^2 to y = (x + 2)^2.
- 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.
▶ Watch this lessonEn 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
Teach this lesson today
An AI tutor that guides with questions instead of just giving answers — all K–12 core subjects, every child in the family.
Start free — no card required