For a function , its graph is the subset of . It differs from a graph in graph theory. A solution curve of a scalar differential equation can be a graph over its independent coordinate.
The map is continuous into the product topology. It maps a compact space onto the graph of a function of a continuous . Hence that graph is compact, whether or not the codomain is a Hausdorff space. Projection to is its continuous inverse.
For a continuous map with Hausdorff space , its graph of a function is closed in the product topology. If , choose disjoint neighborhoods of those two points in . Continuity supplies a neighborhood of whose image lies in the neighborhood of ; its product with the other neighborhood misses the graph.
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The graph of a function is a visual representation of the relationship between the inputs (independent variables) and outputs (dependent variables) of that function. In coordinate geometry, a function can often be represented in a two-dimensional space using a Cartesian coordinate system, where the x-axis represents the independent variable (often denoted as \( x \)) and the y-axis represents the dependent variable (often denoted as \( f(x) \) or \( y \)).