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If a function has vertical asymptotes, can it be continuous?

User Tkachuko
by
7.8k points

1 Answer

1 vote

we have that

if a function has vertical asymptotes

then

The function is not continuous

Example

f(x)=1/x

The function has a vertical asymptote at x=0

The domain is the interval (-infinite,0) U (0, infinite)

The value of x=0 is not included in the domain

therefore

The function is not continuous

User Jens Erat
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7.1k points