anonymous
  • anonymous
How do you know or find if there is a hole in a rational function?
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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Luigi0210
  • Luigi0210
When there are like equations in the denominator and numerator, such as: \[\frac{x-2}{(x-1)(x-2)}=0\] The x-2 would cancel leaving a hole at x=2 and the new function would be: \[\frac{1}{x-1}\]
tkhunny
  • tkhunny
I like to think of it this way: 1) If a value for x makes the denominator zero (0), it is a POTENTIAL vertical asymptote. 2) If that value for x also makes the numerator zero (0), it is a hole, and not an asymptote at all.
tkhunny
  • tkhunny
I also like to think of it this way, using Luigi's example: These two functions are EXACTLY the same \(y = \dfrac{(x-2)}{(x-1)(x-2)}\) \(y = \dfrac{1}{x-1}\) EXCEPT at x = 2 where the first one fails to exist.

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goformit100
  • goformit100
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