Sketch from Conditions
Build a graph that satisfies every condition. There are infinitely
many right answers, so nothing here is compared against one particular
curve — each condition is checked against what you drew, and told back to
you one at a time.
Drag the handles. Select one and the tools under the
graph say what you can do with it: a hollow dot, a solid dot, or an end that
runs off the screen.
The conditions
Check my sketch
Start over
Problems
Write your own conditions
One per line, or separated by semicolons. Write them as you would say
them: lim(x->2-)=3, lim(x->2+)=-1,
f(2)=1, f(0)=undefined,
lim(x->1)=inf, lim(x->inf)=0.
Conditions
Use these conditions
Sketch from Conditions
You are given facts about a function — one-sided limits, values, what it
does far out — and you draw a function that has all of them. This
is the exercise that is hard to grade on paper and impossible to
self-check, because there are infinitely many right answers.
Nothing is compared to a model answer
Each condition is checked against your drawing on its own. When one fails,
the page says what your graph does there instead — "your graph approaches
2 at x = 2 from the left, not 3" — because that is something you can
act on, and a cross is not.
The pieces
The canvas is cut at every x the conditions mention, and each piece
starts undrawn . Drag any of its handles to draw it. A piece you have
not touched claims nothing — otherwise a problem asking for
Hollow dot ○ — the graph approaches this height but does not take
it: a one-sided limit with no value there.Solid dot ● — the function is this value here.Dashed horizontal line ⋯ — add one for a limit at infinity and
drag it to the height you want. It is notation : the check reads
the height your curve runs out at, never the line. It earns its keep
because drawing it is part of the answer, and because a far end dragged
near one snaps onto it, so the curve and the line cannot disagree by a
pixel you can't see.Arrow ↑ ↓ — the graph runs off the screen: an infinite limit.
The piece is redrawn running off that edge and leaving
vertically , and the dashed line at that x darkens into
the vertical asymptote it now is. Dragging an end very high is
not the same thing, and the check says so.
Two solid dots at the same x at different heights is the mistake
worth making once: a function cannot have two values there. The page names
it rather than quietly picking one.
Keyboard
Tab Move between handles
↑ ↓ Move the selected handle
← → Move an interior handle sideways
Enter Check the sketch
? This dialog
Setting a problem
The conditions are in the URL, so you can set one:
?c=lim(x->2-)%3D3;lim(x->2%2B)%3D-1;f(2)%3D1;lim(x->inf)%3D0
See docs/url-api.md for every parameter.
Close