Supported operators: + - * / ^, parentheses, and constants pi, e.
Functions: sin cos tan, asin acos atan, sqrt abs,
ln log exp, floor ceil round, pow(a,b) min(a,b) max(a,b).
This tool samples your function across a chosen x-range and plots points on a coordinate plane. Each row is calculated using:
- f(x) or g(x) is the expression you type.
- For each x value: y = f(x) (and optionally y = g(x)).
- Sampling uses: x = xmin + k·step, for k = 0, 1, 2 …
- The graph is built from the computed (x, y) pairs.
- Type a valid expression in f(x). Use
xas the variable. - Optionally add g(x) to compare two curves.
- Set x Minimum, x Maximum, and Step Size.
- Choose line or scatter, then adjust points, grid, and smoothness.
- Press Make Graph to generate the chart and table.
- Use Download CSV or Download PDF to export results.
Example for f(x) = x^2 from x = -3 to 3 with step 1.
| x | f(x) |
|---|---|
| -3 | 9 |
| -2 | 4 |
| -1 | 1 |
| 0 | 0 |
| 1 | 1 |
| 2 | 4 |
| 3 | 9 |
1) What this tool plots
This graph maker turns your math expression into a clean x–y curve. You can plot one function, or compare two functions on the same axes, using a shared domain and step size.
2) Input formats supported
Type expressions like x^2, sin(x), log(x), sqrt(x), abs(x), and combinations such as 3*sin(x)+2. Constants pi and e are accepted, and parentheses control order. Trig functions use radians, so sin(pi/2) evaluates to 1.
3) Sampling and resolution
The calculator samples points from x-min to x-max using step. For example, a range of 0 to 10 with step 0.1 produces 101 samples. Smaller steps add detail but increase compute time and file size. As a practical rule, aim for a few hundred to a few thousand points for fast plots.
4) Discontinuities and invalid values
If the expression becomes undefined (like 1/(x-2) at x=2, or sqrt(x) for negative x), those points are skipped so the chart breaks naturally instead of drawing misleading spikes. This is especially helpful when graphing asymptotes, piecewise-like behavior, and domain-restricted functions.
5) Axes, scaling, and labels
You can choose automatic y-scaling or lock a fixed y-range when comparing shapes. Add a title, x-label, y-label, and a grid for readability. A point radius option lets you highlight sampled data points for teaching and checking. When using fixed scales, keep the y-range wide enough to avoid clipping peaks.
6) Comparing two functions
Use the second expression field to compare related models, like x^2 versus x^2+2x+1. Because both curves share the same x values, differences are visually consistent across the domain. This makes it easy to validate identities, test transformations, and see how parameters affect curvature.
7) Exporting and sharing results
Download a CSV of computed points for spreadsheets, or generate a PDF report for printing. The CSV includes x and y columns (and y2 when enabled), making it easy to reuse the exact data for labs, homework, and quick verification. The PDF provides a summary of inputs and a readable list of sampled values for documentation.
1) Can I graph more than one function at once?
Yes. Enable the second expression field and enter g(x). Both curves use the same x-min, x-max, and step values, so the comparison stays consistent.
2) What does the step value do?
Step controls how far x increases between samples. Smaller steps create more points and smoother curves, while larger steps create fewer points and faster results.
3) Why are parts of my graph missing?
Missing segments usually mean the expression is undefined for some x values, such as division by zero or taking a square root of a negative number. Those points are skipped to avoid misleading lines.
4) Do trig functions use degrees or radians?
They use radians. For degree input, convert first. Example: sin(30°) becomes sin(pi*30/180), which is sin(pi/6).
5) How do I keep the y-axis from jumping around?
Choose a fixed y-range and enter y-min and y-max. This locks scaling across runs, which is useful when testing parameter changes or comparing two expressions.
6) What’s included in the CSV and PDF downloads?
CSV exports the computed table of x, f(x), and optional g(x). PDF provides a summary of inputs and a readable list of sampled values, helpful for printing or attaching to reports.