Graph of y = 1/x (Reciprocal Function)
The graph of y = 1/x is a hyperbola with two branches, in the first and third quadrants, that approach the asymptotes x = 0 and y = 0 but never touch them.
At a glance
| What it is | Graph y = 1/x online and see its two branches and asymptotes at x = 0 and y = 0. Learn the domain, range and transformations. Free. |
|---|---|
| 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
| Vertical asymptote | x = 0 |
|---|---|
| Horizontal asymptote | y = 0 |
| Domain | All real numbers except 0 |
| Range | All real numbers except 0 |
| Symmetry | Odd function: rotational symmetry about the origin |
Transformations
y = a ÷ (x − h) + k moves the asymptotes to x = h and y = k. A negative a flips the branches into the second and fourth quadrants.
How to use it in Plotline
- The graph of y = 1/x 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 is there a gap at x = 0?
Division by zero is undefined, so y = 1/x has no value at x = 0. As x gets close to 0 the graph shoots up or down toward the asymptote.
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
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