Graph Plotter

Visualize mathematical functions and equations

Quick answer

Graph Plotter

Input any JavaScript mathematical expression using x as the variable. The calculator will plot the function for the given range of x values.

Formula

y = f(x)

Example Functions:

  • x*x - Quadratic function
  • Math.sin(x) - Sine wave
  • Math.cos(x) - Cosine wave
  • Math.exp(x) - Exponential
  • Math.log(x) - Natural logarithm
  • 1/x - Reciprocal function

📈Formula

y = f(x)

💡How it works

Input any JavaScript mathematical expression using x as the variable. The calculator will plot the function for the given range of x values.

ℹ️ What is Graphing Calculator?

A graphing calculator plots mathematical functions on a coordinate plane, visualizing equations like y = f(x) to understand behavior: where a function crosses the x-axis (roots), where it peaks or troughs (extrema), inflection points, asymptotes, and intervals of increase or decrease.

📐 Formula

y = f(x) | Roots where f(x) = 0 | Extrema where f'(x) = 0
f(x)— The mathematical function to plot
Domain— Range of x values to display on the graph
Range— Y values corresponding to the domain
Intercepts— x-intercept (y=0) and y-intercept (x=0)

✏️ Worked Example

Function: y = x² − 4x + 3
  1. 1y-intercept: set x=0 → y = 0 − 0 + 3 = 3. Point: (0, 3)
  2. 2x-intercepts: solve x² − 4x + 3 = 0 → (x−1)(x−3) = 0 → x = 1 or x = 3
  3. 3Vertex (minimum): x = −b/2a = 4/2 = 2 → y = 4−8+3 = −1. Vertex: (2, −1)
  4. 4Opens upward (a = +1 > 0)
✅ Result: Parabola opening up, vertex at (2,−1), crosses x-axis at x=1 and x=3

💡 How to Interpret Results

  • ▸Where the curve is above the x-axis, f(x) > 0; below means f(x) < 0.
  • ▸Steeper slope = faster rate of change at that point.
  • ▸Local maxima/minima occur where the curve changes direction (derivative = 0).
  • ▸Asymptotes (vertical/horizontal) show where the function approaches infinity or a limit.
  • ▸Intersection of two curves shows solutions to f(x) = g(x).

❓ Frequently Asked Questions

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