Video: Finding the One-Sided Limit of a Function from Its Graph at a Point If the Limit Exists

Determine lim_(𝑥 → −4⁻) 𝑓(𝑥).

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Video Transcript

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

We don’t know what the function 𝑓 of 𝑥 is. So we’re going to try and use the graph we’ve been given to work out this limit. We’re interested in the point negative four on the 𝑥-axis. If we look at the point 𝑥 is negative four, we can see that the function is undefined. However, we’re asked to work out the limit as 𝑥 approaches negative four from the left. So if we look at our graph, we can see that the graph approaches the value negative three. It doesn’t actually get to negative three; but it’s approaching negative three. And so the limit as 𝑥 approaches negative four from the left of 𝑓 of 𝑥 equals negative three.

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