# How do you find points of discontinuity in rational functions?

Rational Functions are discontinuous when their denominators become zero; for example,

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To find points of discontinuity in rational functions, we need to identify values of x that make the denominator equal to zero. These values are called the potential points of discontinuity. To determine if these points are actual points of discontinuity, we check if the numerator also approaches infinity or a finite value as x approaches these potential points. If the numerator approaches infinity or a finite value, then the function has a hole or removable discontinuity at that point. If the numerator approaches positive or negative infinity, then the function has a vertical asymptote at that point. If the numerator approaches different finite values from the left and right sides, then the function has a jump discontinuity at that point.

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