Domain & Range

Which x-values go in, and which y-values come out?

The domain of a function is the set of all valid inputs (x-values). The range is the set of all possible outputs (y-values). For f(x) = √x, the domain is x ≥ 0 because you cannot take the square root of a negative number.

On a graph, the domain is the horizontal extent of the curve, and the range is its vertical extent. Some functions have restricted domains — holes, asymptotes, or square roots that cut off part of the graph.

Ask the AI anything — try "What is the domain of 1/(x − 2)?" or "Why can't the range of x² include negative numbers?"

Related Topics

What is a Function?Rational FunctionsAbsolute Value Functions

Suggested Lessons

Slope Quadratic Equations Unit Circle Word Problems
What is domain?
The domain is the set of all x-values for which the function is defined. For example, √x has domain x ≥ 0 (no negative inputs), and 1/x has domain all real numbers except x = 0 (division by zero is undefined).
What is range?
The range is the set of all y-values the function can produce. For x², the range is y ≥ 0 because a square is never negative. For √x, the range is also y ≥ 0.
How do I find domain from a graph?
Look at how far left and right the curve extends along the x-axis. If the curve stops at a certain x-value, that is a domain boundary. Vertical asymptotes (dashed lines) mark x-values excluded from the domain.
What does "all real numbers except" mean?
It means the function works for every x-value except specific ones where it breaks — like division by zero or taking the log of zero. We write this as x ∈ ℝ, x ≠ 2 or (−∞, 2) ∪ (2, ∞).
What can it graph?
It can plot explicit, implicit, and parametric functions, add points and geometry, and animate sliders on the same graph.
Can I use voice or a photo?
Yes. You can talk to the tutor, upload a worksheet or handwritten problem, and let the graph update from that input.
Will it explain the steps?
Yes. The AI explains what it is drawing and why, so you see the answer on the graph instead of getting only a final number.