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# Graph

The graph of a function is the representation of the function using the Cartesian coordinate system. It is the collection of all points $$\big(x,f(x)\big)$$ where $x$ ranges through $D_f$.

The graph of $x\mapsto 1/(x-1)^2.$

Because $f(x)$ takes only one value, each $x$-coordinate in the graph has only one corresponding $y$-coordinate. Any vertical line intersects the graph at most once.

The blue circle on the left is not the graph of a function since the red vertical line intersects it twice. The semi-circle on the right is the graph of a function.