Use the graph of f in the figure to evaluate the function or a...

Question

Use the graph of f in the figure to evaluate the function or analyze the limit.

lim x→3^− f(x)

Accepted Answer

Hi everyone, let's take a look at this practice of problem dealing with limits. This problem says, use the following graph to find the limit as X approaches 0 from the left of F of X. Below the question, we're given a graph that has our function F of X drawn on it, and it is a piecewise function. It consists of three different segments. The first segment is linear and begins at the point of -4-4, and goes to the point of -2.0. The next segment is a parabola that opens upwards, and it begins at the point of -2.0 and goes to the point of 2.0. It also has a minimum located at the point of 0.3. However, this point is excluded from the function, and we have an individual point at X equals to 0, and that it's located at 0.1. For the last segment, we have a line that begins at the point of 2.1 and goes to the point of 10. minus 5, and that initial point of 2.1 is excluded from our function. We're also given 4 possible choices as our answers. For choice A, we have 0, for choice B, we have -1, for choice C, we have -2, and for choice D, we have minus 3. Now, we need to determine the limit as X approaches 0 from the left of F of X. So, what we're going to do is use our graph to determine that limit. So, we're going to be starting to the left of X equal to 0, since we're approaching the value of X equal to 0 from the left, and we're just going to follow our function. To see what value it approaches. In doing so, we noticed that it is approaching a value of -3. So that means that the limit As X Approaches 0 from the left of F of X. It's going to be equal to -3. And so that is actually the answer that I'm looking for. And if I look at my answer choices, this actually corresponds to answer choice D. It should be noted, however, that the value of our function when X is equal to 0, is actually equal to -1. So, the value of the function does not affect the value of our limit. So the limit, if you recall, is the value that the function is approaching, even though it may be equal to a different value at that point. So keep that in mind when you're dealing with limits. So I hope that this explanation has been useful, and I'll see you in the next video.

Use the graph of f in the figure to evaluate the function or analyze the limit. <IMAGE>
lim x→3^− f(x)

Key Concepts

Limits

One-Sided Limits

Graphical Analysis

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