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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, xΒ², xΒ³, 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 = xΒ² βˆ’ 4x + 3. See zeros at x = 1, x = 3 β€” confirm with the quadratic formula.

Compare multiple curves​

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

Explore transformations​

y = xΒ² vs y = (x βˆ’ 2)Β² vs y = 2(x βˆ’ 2)Β². See how shifting and scaling work geometrically.

Teach calculus concepts​

Plot f(x) and f'(x) together β€” visual intuition for what derivatives mean.

How it works​

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

Examples​

Input: y = xΒ² βˆ’ 4

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

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

Output: Two waves; sin starts at 0, cos starts at 1; they intersect at x β‰ˆ 0.785 (Ο€/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 β€” no vertical line drawn through asymptote. Toggle "connect through ∞" if you want lines anyway (less mathematically honest).

Implicit equations (e.g. xΒ² + yΒ² = 1)?

Limited support β€” solve for y: y = ±√(1 βˆ’ xΒ²) and plot two branches. Tool offers "implicit" mode for circles / ellipses; complex implicit curves need a CAS.

Polar plots?

Yes β€” toggle "polar" and use r = f(ΞΈ). Useful for spirals and rose curves.

Scaling β€” 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) β€” 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 (2Ο€ for sin) β€” graph wraps cleanly.
  • For functions with discontinuities, increase sample count to 1000+ β€” too few samples can miss the discontinuity.

Try it now​

The full equation-grapher runs in your browser at https://ztools.zaions.com/equation-grapher β€” no signup, no upload, no data leaves your device.

Open the tool β†—

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