Labs / Mathematics
Graph Transformer
Pick a parent function, then pull the four sliders to build y = a·f(b(x − h)) + k. The faint dashed curve is the original, so you can watch every stretch, flip, and slide. Drag the graph itself to shift it, or turn on “Animate steps” to apply one transformation at a time.
y = xidentitydom all real xran all real y
What to try
- Make a negative. Which axis does the curve flip across, and why is it that one?
- On y = x², does changing h shift the parabola left or right — and does the sign of h feel backwards to you?
- Compare a (the a-slider) with b. Both can “stretch” the graph — so why do they look completely different?
- Switch to √x and drag b below zero. What happens to the domain, and where does the graph disappear to?
- With sin x, can you find values of a and k that keep the whole wave above the x-axis?