What is the name for a graph that represents a function?

A graph that represents a function is called a function graph, or more formally, the graph of a function.

In mathematics, the graph is the collection of ordered pairs (x, y) produced by the function, where y equals f(x). Each input x is paired with exactly one output y. When both values are real numbers, the pairs are plotted as points on a coordinate plane, often forming a line, curve, or other shape.

A function graph is not necessarily a line graph. A line graph usually describes a chart showing changes over time or across categories, while a function graph specifically represents a mathematical relationship between inputs and outputs. Bar graphs and data graphs are broader chart types and do not automatically represent functions.

One useful test is the vertical-line test: if any vertical line crosses the plotted shape more than once, the graph does not represent a function of x, because one input would have multiple outputs.