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# Visually determining vertical asymptotes (old)

Video transcript

Given the graph of y equals
f of x pictured below, determine the equations of
all vertical asymptotes. So let's see what's
going on here. So it looks like
interesting things are happening at x equals
negative 4 and x equals 2. At x equals negative 4, as
we approach it from the left, the value of the function
just becomes unbounded right over here. It looks like as we
approach x equals negative 4 from the left, the value of
our function goes to infinity. Likewise, as we approach
x equals negative 4 from the right, it looks like
the value of our function goes to infinity. So I'd say that
we definitely have a vertical asymptote
at x equals negative 4. Now let's look at x equals 2. As we approach x
equals 2 from the left, the value of our function once
again approaches infinity, or it becomes unbounded. Now from the right we
have an interesting thing. If we look at the limit from
the right right over here, it looks like we're
approaching a finite value. As we approach x equals
2 from the right, it looks like we're approaching
f of x is equal to negative 4. But just having a one-sided
limit that is unbounded is enough to think about
this as a vertical asymptote. The function is not
defined right over here. And as we approach it
from just one side, we are becoming unbounded. It looks like we're approaching
infinity or negative infinity. So that by itself, this
unbounded left-hand limit or left-side limit by
itself, is enough to consider x equals 2 a vertical asymptote. So we could say that there's
a vertical asymptote at x equals negative
4 and x equals 2.