What quantity did you change?
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.
Labs / Mathematics / Graph Transformer
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.
Why it matters
Why explore this?
Mathematics helps us describe patterns precisely and predict what comes next. This model turns an abstract relationship into something you can change and observe.
Explore
Try the model
y = xidentitydom all real xran all real y
Investigate
Questions to test
Predict first, try it in the model, then use what you observe to answer.
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?
Explain
Make sense of what happened
State the pattern in words, test it with another example, and then connect it to the mathematical rule or representation shown in the model.
Check
Before you leave
What pattern did you observe?
Does the pattern work for another example?
If you can answer all three using evidence from the model, you understand the main idea. If not, return to Explore and change one setting at a time.