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we're asked to select the correct description it looks like all the descriptions deal with what is the limit of f of X as we approach 6 from either the right hand side or from the left hand side so let's think about that so first let me just do the left hand side so the limit of f of X as we approach 6 from the left hand side what is this going to be equal to so as we approach from the left hand side we can see well f of 4 is little under 2 f of 5 is it looks like it's around 3 f of 5.5 is it looks like it's a lot higher f of 5.75 even it's just going off the chart so it looks like this is going unbounded in the positive direction so we could say that this right over here is positive in infinity and if we were to go if we were to think about the limit of f of X as we approach 6 from the right side what is this going to be well here f of 7 it's negative f of 7 point 5 is even more negative F of 7 so f of 6.5 is even more negative not 7 point F of 6.5 is even more negative F of 6.1 is even more negative than that f of 6.01 would be even more negative than that so it looks like this is unbounded in the negative direction so this is negative infinity so let's see which of our choices match up to that so the way they listed it they listed the right the the right the limit from the right direction or 1st so that's this one so the limit of f of X is x approaches 6 from values greater than 6 we have negative infinity so that is these two choices these two choices say that so we're going to rule out those two choices and then we think about as we approach 6 from the left hand side we see that we go to positive infinity and that is this choice right over here so we rule out that 1 and that is what we will pick