# Calculadora gráfica

> Grafique varias funciones, curvas polares y paramétricas; desplace y amplíe la vista; encuentre raíces, intersecciones, extremos y áreas.

Versión interactiva: https://www.calcopenly.com/es/math/graphing-calculator
Tema: Calculadoras de matemáticas

Plot up to six functions of x on one set of axes, alongside polar curves such as r = 1 + cos(θ) and parametric curves such as (cos(t), sin(2t)). Drag to pan, scroll or pinch to zoom, and hover to read each function's value, which is recomputed in 50-digit decimal at the pointer.

Below the plot, the calculator lists the roots, turning points and intersections visible in the current window, found by bisection on sign changes. It can also plot the derivative of the first function and shade the area under it between two limits, reporting the integral by Simpson's rule.

Trigonometric functions take radians here, as in most graphing software; type pi/2 rather than 90.

## Datos

- **f(x)**
- **x**

## Resultados

- f(x) — resultado principal

## Ejemplos resueltos

### Cubic at 2

- f(x): x^3 - 3x
- x: 2
- **f(x): 2**
- Fuente de comprobación: 8 − 6

### Sine at π/2

- f(x): sin(x)
- x: pi/2
- **f(x): 1**
- Fuente de comprobación: sin(π/2) = 1; the plotter works in radians

### Rational function

- f(x): 1/(x-1)
- x: 3
- **f(x): 0.5**
- Fuente de comprobación: 1/2

## Preguntas

### How do I find where two graphs intersect?

Enter both functions and look at the 'Points of interest' table under the plot. It reports numerical candidates in the visible window, with coordinates rounded to 8 significant figures; this display precision does not guarantee that accuracy. Sampling can miss tangencies or closely spaced intersections. Zoom or pan to inspect the region, and check important solutions in the original equations.

### Can it plot polar and parametric equations?

Yes. Start a line with r = to plot a polar curve in θ (for example r = 2 sin(3θ) draws a three-petal rose), or write a pair in brackets such as (cos(t), sin(t)) for a parametric curve, traced for t from −2π to 2π.

### Why does tan(x) have gaps?

tan(x) has vertical asymptotes at x = π/2 + kπ, where it jumps from +∞ to −∞. The plotter breaks the line wherever consecutive samples jump by more than one and a half screen heights, so it doesn't draw false vertical lines across the asymptotes.

### ¿Qué precisión tiene «Calculadora gráfica»?

La precisión depende de tus datos y de los supuestos del método. El cálculo decimal usa 50 cifras significativas, pero las estimaciones, los métodos numéricos y los datos de origen pueden ser menos precisos; el redondeo mostrado no elimina esos límites. Ejemplos resueltos comprobados con fuentes independientes: 3. Por ejemplo, «Cubic at 2» se comprueba con 8 − 6.

### ¿De dónde procede el método?

OpenStax Precalculus 2e — Functions, function notation and graphs; Implementation: adaptive sampling with discontinuity breaks; values at a point recomputed in 50-digit Decimal.

## Fuentes

- [OpenStax Precalculus 2e — Functions, function notation and graphs](https://openstax.org/books/precalculus-2e/pages/1-1-functions-and-function-notation)
- Implementation: adaptive sampling with discontinuity breaks; values at a point recomputed in 50-digit Decimal