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Function Equation Plotter

· Last updated：2026-06-19

Plot one or more y=f(x) expressions, mark roots and extrema, and generate SVG-ready graph output

Details

What this tool helps you do

Parses one or more equations such as sin(x)/x or x^2-2x, samples them over a shared domain, identifies approximate roots and local extrema, and can estimate an integral area for one selected series.

Execution

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Samples

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Written by the Elysia Tools team
Math502
Graph27

Tool usage guide

Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Category
Math & Numbers
Input types
textarea, number
Output type
html
Sample coverage
4
API ready
Yes

Overview

The Function Equation Plotter is an online mathematical tool designed to parse and plot one or more y=f(x) expressions on a shared coordinate system. It automatically identifies approximate roots and local extrema, estimates the definite integral area for a selected series, and generates an SVG-ready graph output.

When to use

  • When you need to visualize and compare multiple mathematical functions on a single set of axes.
  • When you want to identify critical points like roots and local extrema without manual calculation.
  • When you need to estimate the definite integral area under a curve and export the resulting graph.

How it works

  1. 1Enter one or more mathematical expressions, such as x^2 - 2*x or sin(x), with each equation on a new line.
  2. 2Define the X and Y axis limits and set the sample count to control the resolution of the plotted curves.
  3. 3Specify the integration range to highlight and calculate the area under the curve for the selected function.
  4. 4Generate the interactive SVG graph displaying the curves, roots, extrema, and shaded integral area.

Use cases

  • Plotting a parabola alongside a sine wave to find their intersection trends and roots.
  • Visualizing the definite integral area of a trigonometric function over a specific interval.
  • Generating clean SVG graphs of mathematical functions for academic reports or presentations.

Examples

1. Plotting a Parabola and Sine Curve

Mathematics Teacher

Background

A teacher wants to show students how a quadratic function and a trigonometric function behave on the same coordinate plane.

Problem

Visualizing the roots and intersection trends of x^2 - 2*x and sin(x) while highlighting the integral of sin(x) from 0 to pi.

How to use

Enter the two equations in the Expressions field, set the X limits from -2 to 4, and configure the integral range from 0 to 3.1416.

Expressions: x^2 - 2*x
sin(x)
xMin: -2
xMax: 4
yMin: -2
yMax: 4
integralFrom: 0
integralTo: 3.1416

Outcome

An SVG graph showing both curves, marked roots, local extrema, and the shaded area under the sine curve from 0 to 3.1416.

2. Analyzing Cubic Function Extrema

Engineering Student

Background

A student needs to locate the local maximum and minimum points of a cubic polynomial for a calculus assignment.

Problem

Finding the critical points of the function x^3 - 3*x on a domain of -3 to 3.

How to use

Input x^3 - 3*x into the expressions box, set xMin to -3 and xMax to 3, and generate the plot.

FAQ

How do I input multiple equations?

Enter each equation on a new line in the Expressions text area.

What mathematical functions are supported?

Standard algebraic operators and trigonometric functions like sin(x), cos(x), and basic powers are supported.

Can I customize the resolution of the graph?

Yes, you can adjust the Sample Count option between 40 and 1200 to change the plotting resolution.

How does the tool calculate the integral area?

It estimates the definite integral between the 'Integral From' and 'Integral To' values for the plotted series.

What format is the output graph?

The tool generates an SVG-ready HTML graph that displays the curves, roots, extrema, and shaded integral area.

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Expressions: x^3 - 3*x
xMin: -3
xMax: 3
yMin: -5
yMax: 5

Outcome

A plotted cubic curve with marked local extrema at (-1, 2) and (1, -2), along with its roots at -1.732, 0, and 1.732.