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{{ printedBook.courseTrack.name }} {{ printedBook.name }} A point of discontinuity of a rational function is a point where the $x$-coordinate makes the function value undefined. Often, this occurs when the $x-$coordinate makes the denominator equal to $0.$ Below is an example.

Since $x=-1$ is not in the domain of the function $y=x+11 ,$ it is a point of discontinuity. There is no way to rewrite the expression so that $x=-1$ becomes a valid input. Therefore, it is called a$f(x)=x−2x_{2}−4 $

Simplify right-hand side

WritePowWrite as a power

$f(x)=x−2x_{2}−2_{2} $

FacDiffSquares$a_{2}−b_{2}=(a+b)(a−b)$

$f(x)=x−2(x+2)(x−2) $

SimpQuotSimplify quotient

$f(x)=x+2$

A removable discontinuity, like the one at $x=2,$ is typically called a hole

in the graph.