Question

How does the vertical line test help to identify functions?

Solution

VerifiedAnswered 1 year ago

Answered 1 year ago

For a given relation, we can always plot that relation on the $XY$-plane as follows: If $y$ is an output corresponding to an input value $x$, then we plot the point $(x,y)$ on the $XY$-plane.

Now by definition of a function, there can't be any points of the form $(x,y_1)$ and $(x,y_2)$ for $y_1\neq y_2$. This in terms of the *vertical line test* says that the vertical line through $(x,0)$ can't intersect more than one point of the plotted function on the $XY$-plane.

Thus we can identify functions using the vertical line test.

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