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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 our route 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 now for the value of our function once again approaches infinity or it becomes unbounded now from the right we have an interesting thing if we 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 but 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