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Determine lim_(𝑥 → −3⁻) 𝑓(𝑥).

Determine the limit as 𝑥 approaches negative three from the left of 𝑓 of 𝑥.

This is an interesting function that we’ve been given. This function is defined at 𝑥 equals negative three to be negative one. But we’ve been asked to evaluate this function as 𝑥 approaches negative three from the left. Remember this superscript means from the left. So we need to do more than just look at the value where 𝑥 equals negative three. We need to look closely at what this function is doing as we approach negative three from the left. So if we follow this function here from the left, as we get closer and closer to the point where 𝑥 equals negative three, this function is actually approaching a different value. It’s approaching the value negative three on the 𝑦-axis.

The two circles that you see where 𝑥 equals negative three means that the function is not defined at these points. It’s only defined at this point where 𝑥 equals negative three. But that doesn’t matter when we’ve been asked what the limit is as 𝑥 approaches a number. So the answer here is negative three. You’ve got to be really careful when answering this type of problem to make sure you’re considering the function as it approaches a value.

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