Graphing Calculator

How the Graphing Calculator Works

This Graphing Calculator lets you enter up to three functions of x and see them plotted together on an interactive coordinate plane. It supports standard operators, parentheses, piecewise-style expressions, trigonometric functions in degrees or radians, logarithms, roots, exponentials, absolute values, and common constants like π and e—while using a locked-down parser so only safe math expressions are ever evaluated.

Safe Expression Parsing & Supported Functions

When you type a function into f(x), g(x), or h(x), the calculator:

• Accepts digits, x, basic operators (+ − × ÷ ^), parentheses, commas, and an approved set of function names and constants.
• Blocks access to JavaScript globals, constructors, or arbitrary code identifiers such as window, document, Function, or Math objects.
• Supports functions like sin, cos, tan, asin, acos, atan, ln, log, sqrt, abs, exp, min, max, and constants pi, e (case-insensitive).
• Normalizes whitespace and invalid tokens so broken expressions simply don't plot instead of crashing the page.

This design gives you the flexibility of a scientific calculator inside a graphing interface, without exposing your browser to unsafe code execution.

Angle Mode, Domain & Sampling

The calculator is built to behave like a proper math tool:

• An Angle Mode toggle lets you choose RAD (radians) or DEG (degrees). All trig functions respect this setting.
• You control x-min and x-max. If you accidentally reverse them, the app automatically swaps the bounds.
• A Samples setting (e.g. 25–5000) defines how many points are used to evaluate each function across the chosen x-range.

Internally, the calculator steps through that range, evaluates each function at each sample, and feeds the valid points into the chart. More samples create smoother curves; fewer samples update faster.

Handling Asymptotes & Undefined Values

Real functions can blow up or break. To display them correctly, the graph:

• Treats any NaN, ∞, or invalid output as a gap instead of drawing a fake spike.
• Leaves visible breaks near vertical asymptotes or removable discontinuities.
• Keeps each function's line separate so intersections and overlaps are easy to see.

The result feels like a classroom graphing calculator: you see real behavior, including discontinuities, instead of a misleading continuous line.

Reading the Graph & Comparing Functions

To make analysis easier, the Graphing Calculator includes:

• A labeled coordinate grid with x- and y-axes, tick marks, and origin lines.
• A clear legend mapping each curve color to f(x), g(x), or h(x).
• A hover tooltip showing the current x and each active function's y-value at that point, with sensible rounding.

This makes it simple to explore intersections, turning points, symmetry, growth, decay, oscillations, and more—by eye—without extra configuration.

Practical Use Cases

This Graphing Calculator is ideal for:

• Algebra and precalculus: polynomials, rationals, exponentials.
• Trigonometry: sine and cosine waves, phase shifts, amplitudes.
• Calculus intuition: limits, discontinuities, and qualitative derivative behavior (slope patterns).
• Quick checks for homework, tutoring, and self-study without installing any desktop software.

Scope & Limitations

To keep it fast, safe, and focused, this tool:

• Supports single-variable functions y = f(x) only.
• Does not compute exact intersections, roots, derivatives, or integrals.
• Does not graph inequalities, shading, or parametric/3D plots.
• Uses double-precision floating point; extremely steep or chaotic behavior may need zooming or more samples.

Educational Insight

Seeing a function is often the fastest way to understand it. By combining a safe expression engine, DEG/RAD control, adjustable domain, and multi-curve overlays, this Graphing Calculator bridges the gap between textbook formulas and visual intuition—perfect for students, teachers, and anyone exploring real-world math.