Graphing Calculator

📈 Graphing basics

Graphing Calculator (Online) — Plot any function of `x`

This Graphing Calculator lets you type a function (like sin(x), x^2 - 4x + 3, or sqrt(x+1)) and instantly visualize it on a coordinate plane. You can pan, zoom, and read approximate values directly from the graph. It’s designed for quick checks while studying algebra, pre‑calc, calculus, or just sanity‑checking homework.

What you can graph

Polynomials: x^2, 3x^3 - 2x + 1
Rational functions: (x+1)/(x-2)
Roots: sqrt(x), x^(1/3) (cube root as a power)
Trig: sin(x), cos(x), tan(x)
Exponentials & logs: 2^x, log(x), ln(x)
Absolute value: abs(x-3)

Formula breakdown (what the calculator actually draws)

When you enter a function y = f(x), the calculator samples many x values across your chosen range (from x_min to x_max). For each sample, it computes y = f(x). Those ordered pairs (x, y) become points on the plane. Then the tool connects nearby valid points with lines to approximate the curve. If the function is discontinuous (for example 1/(x-2)), the calculator avoids drawing a line across the jump by detecting when values are not finite or when the y‑change between neighbors is too large.

The core workflow is:

Choose a window (x-range and y-range).
Sample x values (hundreds to thousands of points).
Compute y for each sample: y = f(x).
Convert coordinates to pixels on the canvas.
Draw a grid + axes + the curve.

Coordinate mapping (math → pixels)

Screens use pixels; graphs use coordinates. The calculator converts an (x, y) into a pixel point (px, py):

px = (x - x_min) / (x_max - x_min) * width
py = height - (y - y_min) / (y_max - y_min) * height

Notice the height - ... part: screens count y downward, but graphs count y upward.

Examples you can copy/paste

Parabola: x^2 - 4x + 3 (vertex near x=2)
Sine wave: sin(x) (try x-range -10 to 10)
Absolute value V-shape: abs(x)
Hyperbola: 1/(x-2) (shows a vertical asymptote at x=2)
Log curve: ln(x) (domain is x>0)

How to use this graphing calculator

Enter your function as the right side of y=... (example: x^2).
Set the window: start with -10 to 10 if you’re unsure.
Click “Graph Function”. You’ll see the curve plus axes and a light grid.
Hover to see coordinates at your cursor.
Pan + zoom to investigate turning points, intercepts, and asymptotes.

Virality notes (why graphs get shared)

Graphs turn a formula into a visual “story”: the drama of an asymptote, the symmetry of a parabola, or the wiggle of a trig wave. People share what they can see. A clean graph + a simple prompt like “Graph your function” is naturally screenshot-friendly.

Common mistakes (and quick fixes)

Missing multiplication: type 2*x (not 2x).
Parentheses: use sin(2*x), not sin 2x.
Domain issues: sqrt(x) needs x ≥ 0; ln(x) needs x > 0.
Exploding values: try Auto‑Fit if the curve shoots off screen.

FAQ

What syntax does this support?
Use x as the variable. Supported functions: sin, cos, tan, abs, sqrt, log (base 10), and ln (natural log). Constants: pi and e. Powers: ^ (or **).
Why are there gaps in my graph?
Many functions are undefined in parts of the number line. The calculator leaves gaps to avoid drawing a misleading line across a discontinuity (example: 1/(x-2)).
How accurate is it?
The curve is a high-quality approximation using dense sampling. For exact roots or symbolic simplification, use a dedicated algebra tool (linked below).
Can I graph piecewise functions?
Not in full piecewise notation yet. A great future upgrade is “multi‑function + piecewise” support (perfect for a Pro tier).

Mini study guide: what to look for on a graph

Intercepts: where the curve crosses the x- and y-axes.
Turning points: local maxima/minima (vertex on a parabola).
Asymptotes: vertical/horizontal lines the graph approaches.
End behavior: what happens as x → ±∞.
Symmetry: even/odd function patterns.

Educational note: This calculator is for visualization. Verify exact results with algebraic methods when precision matters.

Enter your function

Sample points (quick check)