MathsEspanol1 min de lecturaActualizado 1 abr 2026
Mastering Function Transformations
Learn how mathematical functions are shifted, stretched, and reflected across the coordinate plane.
Puntos Clave
- Adding a constant outside the function shifts it vertically.
- Adding a constant inside the function shifts it horizontally (in the opposite direction).
- Multiplying by a constant stretches or compresses the graph.
- A negative sign creates a reflection over the x-axis or y-axis.
What are Parent Functions?
A parent function is the simplest algebraic shape of a given type, such as f(x) = x² for a parabola, or f(x) = |x| for an absolute value V-shape. Function transformations modify these basic building blocks.
Translations (Shifts)
A translation moves the graph without altering its shape or orientation. For y = f(x) + k, the graph moves up if k is positive and down if k is negative. For y = f(x - h), the graph moves to the right if h is positive (e.g., f(x-3) is right 3) and to the left if h is negative.
Dilations (Stretches and Compressions)
A dilation changes the size or scale of the graph. For y = a * f(x), if |a| > 1, the graph is vertically stretched (taller and thinner). If |a| < 1, it is vertically compressed (shorter and wider).
Reflections
Reflections flip the graph. A negative sign placed in front of the function, y = -f(x), reflects the graph vertically across the x-axis. A negative sign inside the function, y = f(-x), reflects it horizontally across the y-axis.
Prueba Estas Calculadoras
algebrafunctionsgraphingmaths