Graphing Calculator
Plot any math function on an interactive graph โ type f(x), zoom in and out, and explore curves, asymptotes and intercepts in real time.
Plot your function
Type any function of x and watch it draw.
Advanced options
The third function and the angle mode take effect when you press Plot Graph; Apply range works straight away. Derivatives and the trace point update the current graph immediately.
x, + โ ร รท, ^ (power), parentheses, sin cos tan log ln sqrt abs, constants ฯ and e.
Example: x^2+2*x+1 ยท trig uses radians (degrees in Advanced options). Plot up to three functions at once.
Each function draws in its own colour โ see the legend above the graph. A dashed curve is that functionโs derivative. Bold lines = x and y axes. Gaps in a curve mean the function is undefined there (e.g. 1/x at x = 0). Turn on the trace point in Advanced options to read exact coordinates off the curve.
Found numerically over the visible x-range: the range is scanned in 800 steps, every sign change is refined by bisection (roots) and every slope change by a golden-section search (peaks and valleys), so values are close approximations rather than exact algebra. A root the curve only touches, like x^2 at 0, is reported when a sampled point lands exactly on it.
Computed from the functions exactly as last plotted (including the angle mode). A dash means the function is undefined at that x.
- The calculator samples your function at hundreds of points across the visible x-range and connects the dots into a smooth curve.
- Points where the function is undefined (like 1/x at x = 0) are skipped, so asymptotes never smear into vertical streaks.
- You can use x, + โ ร รท, ^ (power), parentheses, sin cos tan log ln sqrt abs, and the constants ฯ and e โ trig uses radians by default, so sin(ฯ/2) = 1; a degrees mode lives in Advanced options.
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How to graph a function
From equation to curve in three simple steps.
Enter any f(x), like x^2 or sin(x).
Zoom in on detail or pick a preset curve.
Spot roots, peaks, valleys and asymptotes.
๐How graphing works
Type any function of x and the calculator draws it instantly โ no equals button needed. For example, type x^2+2*x+1 and you’ll see a parabola shifted left by 1 and up… well, try it!
The curve passes through the point (3, 9) โ
Behind the scenes, the calculator samples your function at hundreds of points across the visible x-range and connects the dots into a smooth curve. Points where the function is undefined (like 1/x at x = 0) are skipped, so asymptotes never smear into vertical streaks.
That is the job of a function graph calculator: hand it any function of x and it hands back the graph โ curve, intercepts, peaks and asymptotes โ drawn entirely in your browser.
You can use the variable x, numbers, the operators + โ ร รท ^ (use * and / if you like), and parentheses. Functions: sin cos tan log ln sqrt abs. Constants: ฯ (or pi) and e. Examples that work: x^2+2*x+1, sin(x)/x, sqrt(x+4), 2*e^(-x). Trig functions use radians by default โ so sin(ฯ/2) = 1 โ or switch to degrees in Advanced options.
Gaps appear where the function has no defined value. The classic example is 1/x at x = 0 โ dividing by zero is undefined, so the curve breaks there instead of drawing a false vertical line. You’ll also see gaps or cut-offs for sqrt of negative numbers and log of zero or negatives. These breaks are correct math, not a bug.
๐Reading the picture: roots, intercepts, peaks and valleys
A root is where the curve crosses the x-axis โ the x value that makes the function zero. The y-intercept is where it crosses the y-axis, at x equals 0. Peaks and valleys are the local high and low points, where the curve turns. The analysis panel under the graph reports all three, found numerically over the visible x-range: the range is scanned in 800 steps, every sign change is refined by bisection for roots and every slope change by a golden-section search for peaks and valleys โ so the values are close approximations, not exact algebra.
One edge case deserves a warning: a root the curve only touches, like x squared at 0, has no sign change to find, so it is reported only when a sampled point lands exactly on it. If a touch-root is missing from the panel, zoom in on the touching point and read it from the trace or the table of values instead of assuming it is not there.
๐งฎThree functions, dashed derivatives and the table of values
You can plot up to three functions of x at once, which is how comparisons are done: plot a function and a shifted copy, or a function and a straight line, and read where they meet. The dashed curve is the derivative of the first function โ the slope of the curve at each x, plotted as a function in its own right: it sits above the axis where the original rises, below it where the original falls, and crosses zero exactly at the peaks and valleys.
The table of values lists x and y pairs for the plotted functions, including the places where a function is undefined โ the gaps that correct mathematics leaves in 1 over x, square roots of negatives and logarithms of zero or negatives. Use the variable x, the operators plus, minus, multiply, divide and power, parentheses, the functions sin, cos, tan, log, ln, sqrt and abs, and the constants pi and e. Trig uses radians by default; switch to degrees in Advanced options. What this tool does not do is just as useful to know: no three-dimensional, polar, parametric or implicit plots, and no step-by-step equation solving โ it plots functions of x, and it plots them well.
Frequently asked questions
How do I graph an equation?
Type your function of x into the input box โ for example x^2 โ and the graph updates instantly. Use the preset buttons to try sin(x), 1/x or xยณ with one click.
What functions and symbols are supported?
x, + โ ร รท, ^ for powers, parentheses, sin cos tan, log (base 10), ln, sqrt, abs, and the constants ฯ and e. Try x^2+2*x+1 or 2*sin(x)+1.
Why is there a gap in my graph?
A gap means the function is undefined at that x โ for example 1/x at x = 0 (division by zero) or sqrt of a negative number. The calculator skips those points so asymptotes don’t draw fake vertical lines.
How do I zoom in or out?
Use the + Zoom in and โ Zoom out buttons to change the view, and โฒ Reset to return to the default โ10 to 10 range on both axes. You can also type exact x and y limits in Advanced options and press Apply range.
Does this use degrees or radians?
Radians by default, like most graphing calculators โ so sin(ฯ/2) = 1 and cos(0) = 1. To work in degrees instead, open Advanced options above the Plot button, switch the trig angle mode to Degrees, then plot again.
Is this graphing calculator free?
Yes โ completely free, no sign-up. Everything runs in your browser, so nothing you type is stored or sent anywhere.
How do I find a root from the graph?
Read the analysis panel under the graph: it lists roots, intercepts and extrema found numerically over the visible x-range. To narrow a root down, zoom in on the crossing and use the trace point or the table of values โ the panel values are close approximations refined by bisection, not exact algebra. A root the curve only touches, like x squared at 0, may not appear unless a sampled point lands exactly on it.
What does the dashed curve mean?
It is the derivative of the first function: the slope of the curve at each x, drawn as a function. Where the original curve rises, its derivative is positive and the dashed curve sits above the axis; where the original falls, the dashed curve sits below it; and it crosses zero exactly at the peaks and valleys, where the slope is momentarily flat.
How many functions can I plot at once?
Up to three functions of x. Plot them together to compare shapes, shifts and intersections โ for example a parabola and the line that cuts it โ and read the meeting points from the analysis panel or the table of values. Each function uses the same syntax: x, the usual operators, sin, cos, tan, log, ln, sqrt, abs, pi and e.
Why does sin of pi over 2 give a different answer in degrees mode?
Because the mode changes what the input number means. In radians, pi over 2 is a quarter turn, and sin of it is exactly 1. In degrees mode the same input is read as 1.5708 degrees, a tiny angle, and sin of it is about {deg_val:.4f}. If a trig result looks far too small, check the mode first โ it is the commonest cause of a correct-looking graph giving wrong-looking values.
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