Graphs
A graph represents a function if it passes the vertical line test.
The vertical line test is checking to make sure every \(x\)-value is paired with exactly one \(y\)-value. If a vertical line intersects the graph at two points, then there is an \(x\)-value that is paired with two different \(y\)-values. Look at the graph below, you will notice that the vertical line is intersecting the graph at the point \((4, 3)\) and \((4, -2)\). The \(x\)-value of \(4\) is paired with the \(y\)-value of \(3\) and the \(y\)-value of \(-2\). This means this graph is not a function.
The vertical line test is checking to make sure every \(x\)-value is paired with exactly one \(y\)-value. If a vertical line intersects the graph at two points, then there is an \(x\)-value that is paired with two different \(y\)-values. Look at the graph below, you will notice that the vertical line is intersecting the graph at the point \((4, 3)\) and \((4, -2)\). The \(x\)-value of \(4\) is paired with the \(y\)-value of \(3\) and the \(y\)-value of \(-2\). This means this graph is not a function.