Grapher
Plot up to three functions, with the derivative, the second derivative,
critical points and a tangent line available on request. Any letter other
than the variable becomes a slider.
Grapher
Type a function and it is drawn. Type another and it joins it. Anything
that is not the variable becomes a slider.
What it does that a plain grapher does not
f ′ and f ″Critical and inflection points are found as roots of f ′
and f ″ and marked on the curve. Points where the function only
touches zero without crossing are not found; nothing is invented.Vertical asymptotes are detected and drawn, and the curve is
never joined across one. A grapher that connects the two branches of
1/x is drawing a line that is not there.Horizontal asymptotes are drawn too, and the two ends are
reported separately because they can differ:
3x /√(x ²+1) approaches 3 on the right and −3 on the left.
They are measured by running x out to ±10⁸ and checking that the
values settle, so a limit that converges very slowly — 1/ln x —
is not claimed.Slant asymptotes as well, by the same measurement: the slope is
what f (x )/x settles at, and the intercept is what
is left once that slope is taken away. A line is not dashed as its own
asymptote — true, and it annotates nothing.A tangent line at a point you can slide.
Embedding it
Everything is in the URL, so a graph can be dropped into a page, a quiz or
a homework problem as an iframe:
<iframe src="https://learnlens.org/calclens/graph/?f=x%5E3-3x&window=-3,3&plot=only"
width="600" height="400" style="border:0"></iframe>
plot=only renders the figure alone — no controls, no chrome.
Leave it off and the reader gets the sliders too, which is what you want
for a demo rather than a static figure. The page reports its own height to
the framing document, so the iframe can size itself.
Giving a class fewer things to switch on
layers= decides which toggles the reader is offered .
It is a different axis from show=, which decides what is
on . A class meeting f ′ for the first time gets
?f=x%5E3-3x&layers=deriv
— one checkbox and nothing else to wander into. layers=none
offers nothing at all, and leaving it off offers everything. The two
combine: show=deriv&layers=none puts the derivative on
screen without letting anyone switch it off.
Keyboard
? This dialog
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