## Vertical Line Test for a Function:

Not every curve in the coordinate plane can be the graph of a function. Using vertical line test, we can figure out whether a given curve is the graph of a function or not.

A function $f$ can have only one value $f(x)$ for each $x$ in its domain. So, no vertical line can intersect the graph of a function more than once.

If $a$ is in the domain of the function $f$, then the vertical line $x=a$ will intersect the graph of $f$ at the single point $(a,f(a))$.

Example 1: Consider the curve in the coordinate plane as shown below:

A vertical line intersects the above curve twice. So, the above curve is not the graph of a function.

Example 2: Similarly, the circle is not the graph of a function, since a vertical line can intersect the circle twice.

However, the upper semicircle and the lower semicircle both are the graphs of functions.

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Vertical Line Test for Functions
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