Horizontal Line Test in Calculus
Given a function (i.e. from the real numbers to the real numbers), we can decide if it is injective by looking at horizontal lines that intersect the function's graph. If any line intersects the graph in more than one point, the function is not injective. To see this, note that the points of intersection have the same y-value (because they lie on the line ) but different x values, which by definition means the function cannot be injective.
Passes the test (injective) |
Fails the test (not injective) |
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