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Equation Grapher

An equation grapher plots a function y = f(x) over a range of x values, drawing the curve at all sampled points. Useful for visualising what a formula does, comparing multiple functions, exploring transformations (translation, scaling), and teaching concepts like asymptotes, intersections, and extrema. The ZTools Equation Grapher accepts standard math syntax (sin, cos, log, exp, x², x³, etc.), plots up to 6 functions on the same axes with distinct colours, and exports the chart as SVG for slides or docs.

Use cases​

Visualise a function from homework​

Plot y = x² − 4x + 3. See zeros at x = 1, x = 3 — confirm with the quadratic formula.

Compare multiple curves​

sin(x), cos(x), tan(x) on one axis. Spot symmetries, intersections, asymptotes.

Explore transformations​

y = x² vs y = (x − 2)² vs y = 2(x − 2)². See how shifting and scaling work geometrically.

Teach calculus concepts​

Plot f(x) and f'(x) together — visual intuition for what derivatives mean.

How it works​

  1. Type equation(s) — y = sin(x), y = x^2, etc. Up to 6 expressions, one per line.
  2. Set range — x range (default −10 to 10), y range (auto-fit by default), grid spacing.
  3. Configure samples — How many points to plot (default 500). More = smoother but slower.
  4. Render + export — SVG chart with axes, gridlines, legend. Download as SVG / PNG.

Examples​

Input: y = x² − 4

Output: Parabola opening up, vertex at (0, −4), roots at x = ±2.

Input: y = sin(x), y = cos(x) on x ∈ [0, 2π]

Output: Two waves; sin starts at 0, cos starts at 1; they intersect at x ≈ 0.785 (π/4).

Input: y = 1/x

Output: Hyperbola with asymptote at x = 0; tool draws each branch separately.

Frequently asked questions​

How does it handle vertical asymptotes?

When |y| jumps above the y range, the curve is broken — no vertical line drawn through asymptote. Toggle "connect through ∞" if you want lines anyway (less mathematically honest).

Implicit equations (e.g. x² + y² = 1)?

Limited support — solve for y: y = ±√(1 − x²) and plot two branches. Tool offers "implicit" mode for circles / ellipses; complex implicit curves need a CAS.

Polar plots?

Yes — toggle "polar" and use r = f(θ). Useful for spirals and rose curves.

Scaling — auto vs manual?

Auto fits the y range to the visible function. Manual gives full control. Logarithmic axes available too.

Privacy?

All plotting in browser.

Tips​

  • For educational use, plot the function plus its derivative (numerical differentiation handled internally) — gives students intuition.
  • For comparing transformations, plot the base function plus the variants on one axis; legend keeps them distinguishable.
  • For oscillating functions (sine, cosine), set x range to a multiple of the period (2π for sin) — graph wraps cleanly.
  • For functions with discontinuities, increase sample count to 1000+ — too few samples can miss the discontinuity.

Try it now​

The full Equation Grapher runs in your browser at https://ztools.zaions.com/tools/equation-grapher — no signup, no upload, no data leaves your device.

Open the tool ↗

Last updated: 2026-05-06 · Author: Ahsan Mahmood · Edit this page on GitHub