Graph the Square Root Function
The graph of y = √x starts at the origin and curves gently upward through (1, 1), (4, 2) and (9, 3); it only exists for x ≥ 0.
At a glance
| What it is | Graph y = √x online and learn its domain, range and key points (0,0), (1,1), (4,2), (9,3). Compare it with y = x². Free graphing calculator. |
|---|---|
| Type | Interactive guide with a calculator |
| Level | High school and college |
| Price | Free, with no account or sign-up |
| Works offline | Yes, after the first visit; installs as an app |
| Made by | Aalok (aalok.builds@gmail.com) |
| Last updated | 1 November 2026 |
Key facts
| Domain | x ≥ 0 |
|---|---|
| Range | y ≥ 0 |
| Key points | (0, 0), (1, 1), (4, 2), (9, 3) |
| Inverse of | y = x² for x ≥ 0 (mirror image in the line y = x) |
How do you shift the square root graph?
y = √(x − h) + k starts at the point (h, k) instead of the origin. A minus sign outside, y = −√x, flips the curve below the x-axis.
How to use it in Plotline
- The graph of y = √x together with y = x² for comparison is already loaded above. Edit the equation in the list to change it.
- Drag the graph to move around, scroll or pinch to zoom, and tap the crosshair to reset the view.
- Hover over or tap the curve to read the coordinates of any point.
- Press Enter to add another equation and compare graphs in different colors.
Frequently asked questions
Why does y = √x stop at x = 0?
Because the square root of a negative number is not a real number, so there are no points to the left of the origin. The domain is x ≥ 0 and the range is y ≥ 0, which is why the curve starts at (0, 0) and only rises to the right.
Is it free?
Yes. The graphing calculator is free with no account and no sign-up: plot as many equations as you like, use sliders, save graphs in your browser and share them by link. It installs as an app and keeps working offline.
Learn more
Related
- Parabola (quadratic) – Graph quadratic functions y = ax² + bx + c online.
- Logarithm – Graph y = ln(x) and y = log(x) online.
- Reciprocal function (1/x) – Graph y = 1/x online and see its two branches and asymptotes at x = 0 and y = 0.
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Plotline is an independent project and is not affiliated with Desmos, Texas Instruments or Casio.