Graphing Calculator
Type up to six functions of x and see them plotted at once. Zoom and pan, let the y-axis fit the curves automatically or set your own window, and have the calculator mark where each graph crosses the x-axis, where two graphs intersect, and where they peak or dip. A table of values sits underneath, and the picture downloads as a PNG or SVG. It runs in your browser. Free, no sign-up.
Use x as the variable: x^2 − 3, sin(x)/x, abs(x), sqrt(x), e^(−x^2), ln(x), 1/x. Functions: sin, cos, tan, sec, csc, cot, asin, acos, atan, sinh, cosh, tanh, exp, ln, log (base 10), sqrt, abs. Constants: pi and e.
Results
- y = sin(x)
- y = x/2
Zeros
Function 1: x = -9.424778, -6.283185, -3.141593, 0, 3.141593, 6.283185, 9.424778
Function 2: x = 0
Intersections
| Functions | x | y |
|---|---|---|
| Function 1 and Function 2 | -1.895494 | -0.9477471 |
| Function 1 and Function 2 | 0 | 0 |
| Function 1 and Function 2 | 1.895494 | 0.9477471 |
Table of values
| x | y1 | y2 |
|---|---|---|
| -5 | 0.9589243 | -2.5 |
| -4 | 0.7568025 | -2 |
| -3 | -0.14112 | -1.5 |
| -2 | -0.9092974 | -1 |
| -1 | -0.841471 | -0.5 |
| 0 | 0 | 0 |
| 1 | 0.841471 | 0.5 |
| 2 | 0.9092974 | 1 |
| 3 | 0.14112 | 1.5 |
| 4 | -0.7568025 | 2 |
| 5 | -0.9589243 | 2.5 |
How to Use the Graphing Calculator
- 1. Enter functions. Type each one as an expression in x:
x^2 - 3,sin(x)/x,abs(x),e^(-x^2),ln(x),1/x. A leadingy =orf(x) =is fine. Use “Add a function” for up to six, each in its own colour. - 2. Set the window. Type x min, x max, y min and y max, or use the buttons to zoom in and out and to pan. “Fit y to the curves” picks a y-range that shows the shape and ignores the runaway tails near an asymptote; typing a y-value turns it off. “Square grid” makes one unit the same length on both axes.
- 3. Choose what to mark. Zeros, intersections between each pair of graphs, and local maxima and minima are found numerically across the window and listed beneath the graph.
- 4. Read the table and export. The table lists the values of every function at evenly spaced x. Download the graph as a PNG or SVG for a report or slide.
What the Calculator Can Find
| Feature | How it is found | Example |
|---|---|---|
| Zeros | Sign changes of f, refined by bisection; touching zeros as minima of |f| | sin x has zeros at −3π, −2π, −π, 0, π, 2π, 3π on [−10, 10] |
| Intersections | Zeros of f − g for every pair of functions | x² and x + 2 meet at (−1, 1) and (2, 4) |
| Maxima and minima | Zeros of the exact derivative where its sign changes | x³ − 3x has a maximum (−1, 2) and a minimum (1, −2) |
Try the starting example: sin x and x/2 cross at x = 0 and x ≈ ±1.8955 (where sin x = x/2), and sin x has maxima at x = −3π/2, π/2 and 5π/2 and minima at x = −5π/2, −π/2 and 3π/2 inside the window. Switch on “Maxima and minima” to list them.
Asymptotes, Domains and Limits
- Asymptotes. The pen is lifted wherever a function is undefined or jumps across a vertical asymptote, so tan x and 1/x show separate branches instead of a false vertical line.
- Domains. A function is drawn only where it has a real value: ln x for x > 0, √x for x ≥ 0. Odd roots of negative numbers are real, so x^(1/3) is drawn on both sides of 0.
- Angles are in radians. For sin of an angle in degrees, enter sin(x*pi/180).
- Numerical features can be missed. Zeros and intersections are searched on a grid of 2,000 points across the window, so a feature narrower than about 1/2,000 of its width, or a tangency that does not cross, may be missed or appear slightly off. Zoom in to check a close call.
Frequently Asked Questions
- How do I graph more than one function?
- Use “Add a function” to add a row, up to six. Each is drawn in its own colour on the same axes, and the calculator lists the intersections between every pair.
- How do I find where two graphs intersect?
- Enter both functions and keep “Intersections” ticked. The calculator solves f(x) = g(x) numerically across the window and lists each crossing point with its x and y values. Widen the window if an intersection you expect is outside it.
- How do I find the zeros or x-intercepts of a function?
- Keep “Zeros” ticked and read the list beneath the graph; each function's x-intercepts are given. For an exact solution of a quadratic, the Quadratic Equation Solver gives the roots in closed form, and the Newton's Method Calculator refines any root to many digits.
- Why is part of my graph missing?
- The function is probably undefined there (a logarithm of a negative number, a square root of a negative, a division by zero), or it lies outside your y-range. Try “Fit y to the curves”, or widen the window.
- How do I zoom and pan?
- Use the Zoom in and Zoom out buttons, which halve or double the window around its centre, and the arrow buttons to move it a quarter of a screen at a time. You can also type exact values into the four window fields.
- Can it graph equations like x² + y² = 1 or inequalities?
- No. It plots functions y = f(x). A circle can be drawn as two functions, sqrt(1 − x^2) and −sqrt(1 − x^2), with the square grid switched on so it looks round.