Why Does a Table Fail the Vertical Line Test

The vertical line test is usually described for graphs, but the same idea applies to tables. A table represents a function when each input value appears with exactly one output value. If the same input is paired with two different outputs, no single vertical line through that input can meet the graph only once, so the relation fails the test. Start by listing the input values in order. Mark any duplicates and compare their outputs. For example, if x = 4 gives y = 7 and also y = 10, the table is not a function. If repeated inputs have the same output, the relation is still a function. Write your conclusion with a reason, not only a label. When graphing, plot each pair and draw a vertical line through the repeated input to see the conflict. Practice with several tables until the check becomes quick and confident.