TwiddleLab / Courses / Math

Functions You Can See

Feed a machine numbers, drag lines and curves, and see how one quantity changes another.

Beginner · 10 lessons · Free, no account needed

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Lessons

1. A Function Is a Machine (5 min): A function is a machine: each input gives exactly one output.
2. Slope Is a Rate (7 min): Slope is how much a line climbs for one step to the right.
3. Where Lines Start (7 min): The intercept b is where a line starts on the y axis: the value at x = 0.
4. Reading Graphs Like Stories (7 min): A graph going up is increasing, going down is decreasing, flat is constant.
5. When Two Lines Meet (7 min): Where two lines cross is their intersection.
6. Curves: When Growth Changes (7 min): When the change itself changes, the graph bends: a parabola.
7. Stretch, Flip, Shift (7 min): y = a(x - h)² + k puts the vertex at (h, k).
8. Fitting a Line to Data (7 min): A model is a simple rule that describes messy data, like a line through a cloud.
9. Zoom In: Slope of a Curve (7 min): Zoom in far enough and a smooth curve looks like a straight line: local linearity.
10. Model the World (7 min): To model something, measure it, pick a family (line or parabola) and fit it.

Lessons are interactive and need JavaScript. Turn it on to play them.