Question

what is domain and range in graphing?

Answer 1

Domain: the set of all possible x-values (inputs) for a relation or function.
Range: the set of all possible y-values (outputs) produced by the relation or function.

How to read them from a graph
- Domain: look left-to-right — find every x-coordinate that the graph reaches.
- Range: look up-and-down — find every y-coordinate that the graph reaches.
- Use open dots or holes to indicate excluded endpoints, closed dots for included endpoints. Express results with interval notation or as a list/union of intervals.

Quick examples
- y = 2x + 1 (a line): domain = (−∞, ∞), range = (−∞, ∞).
- y = x^2 (a parabola with vertex at (0,0)): domain = (−∞, ∞), range = [0, ∞).
- y = √x: domain = [0, ∞), range = [0, ∞).
- y = 1/x: domain = (−∞, 0) ∪ (0, ∞), range = (−∞, 0) ∪ (0, ∞).
- Circle x^2 + y^2 = 4: domain = [−2, 2], range = [−2, 2].

Notes
- For a function, each domain x has one output y (vertical line test helps check this).
- From an equation, exclude x-values that make denominators zero or produce invalid operations (like negative inside an even root).