Touch the rule.
See the consequence.
A deliberately small lab for building intuition before symbolic work. No hidden answer key—change one variable, make a prediction, then explain the visual.
f(x) = 1x + 0
Set the slope to −2 and intercept to 3. Predict f(4) before moving the input slider.
Say your prediction aloud first. Then use the graph to check only the claim you made—not a different, easier question.
A tangent is a limit, not a magic line.
Use the derivation after you have moved the graph. It connects an average rate over a tiny interval to the local rate you read above.
A step-by-step visual explanation, rendered in this page.
Press play to build the idea one claim at a time.
Retrieval protocol
Name the behavior, not the graph’s vibe.
Choose the family from its defining change rule. A correct answer only counts when you can name the invariant that made it correct.
For equal input steps, the output rises by +7 every time.