About the Function Graph Plotter
What is the Function Graph Plotter?
A graph shows how a function's output f(x) changes as x changes, making it easy to see where the function rises and falls, where its turning points are and where it crosses the x-axis (its roots). Plotting is the quickest way to understand an unfamiliar formula.
Type a function using x, choose the range and the number of points, and the plotter draws the curve and lists a table of x and f(x) values. It reports the lowest and highest values in the range and counts sign changes, each of which marks a root between two sample points.
How to use the Function Graph Plotter
- Function f(x) — for example x^3 - 2x or sin(x)/x. (sample: x^2 - 4x + 3)
- x from (sample: -1)
- x to (sample: 5)
- Number of Points — more points give a smoother curve (up to 201). (sample: 25)
- Press Plot Function (results also refresh as you type). The result card shows the Range of f(x) Shown, along with Minimum f(x), Maximum f(x), Sign changes (approx. roots) and Undefined points.
Formula used
xᵢ = start + i × (end − start) ÷ (points − 1)
- i = 0, 1, 2, … up to points − 1
- f(xᵢ) = the value of your function at each sample
Supported syntax: + − * / ^, brackets, implicit multiplication (2x, 3(x + 1)), the constants pi and e, and the functions sin, cos, tan, asin, acos, atan, sinh, cosh, tanh, sqrt, cbrt, abs, exp, ln, log, log2, floor, ceil and round.
Worked example
These are the sample values already filled in the calculator above, and the result it returns for them:
| Input | Sample value |
|---|---|
| Function f(x) | x^2 - 4x + 3 |
| x from | -1 |
| x to | 5 |
| Number of Points | 25 |
| Result | Value |
|---|---|
| Range of f(x) Shown | -1 to 8 |
| Minimum f(x) | -1 |
| Maximum f(x) | 8 |
| Sign changes (approx. roots) | 2 |
| Undefined points | 0 |
Tips for using the Function Graph Plotter
- Trigonometric functions use radians: plot sin(x) from 0 to 6.2832 (2π) for one full wave.
- Where f(x) is undefined (for example 1/x at 0 or sqrt(x) for negative x), the table says so and the point is skipped.
- A sign change means a root lies between two samples; narrow the range around it and add points for a closer estimate.