Check whether each input has exactly one output
If any input maps to more than one output, it is not a function
Use the vertical line test for graphs
If any vertical line intersects the graph more than once, it is not a function
If every vertical line intersects the graph at most once, it is a function
Solve the equation for y and see whether y is uniquely determined by x
Look for expressions that create multiple outputs for the same x, such as square roots with both positive and negative values
Check for implicit equations where one x value may produce two or more y values
Verify that restricted domains do not allow repeated x values with different outputs