Finding Limits Graphically

Which of the follo...

Question

Finding Limits Graphically

Which of the following statements about the function y = f(x) graphed here are true, and which are false?

j. limx→2− f(x) = 2

Accepted Answer

Below there. Today we're going to solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. Determine the valididity of the following statement based on the given graph of Y equals FX. The limit as X approaches -1 from the right of F of X is equal to 2. Awesome. So it appears for this particular prompt we're ultimately trying to take our statement, which once again is the limit, as X approaches -1 from the right of F of X equals 2, and we're asked to prove whether or not this statement is true or false using our given. of Y equals F of X. So now that we know that what we're ultimately trying to solve or we're either trying to prove that the statement is either a true or B false, let's take a moment to quickly investigate our graph to see what exactly is going on to help us better visualize what's happening. And as you can see, we can see that what appears to be two separate curves because our curve for Y equals F of X is represented in red. And even though it looks like two separate curves, it's technically the same curve. It's just it's split because when we look at our graph, it starts at -11 or -1.1. And it starts at a solid point and then it goes to 01, where there's a hole or a discontinuity. So that means that the curve will jump and it jumps to 0.0, and then it curves upward to 1.1, where there appears to be a second hole, and then it curves down to 0.2, where there is another hole, and there's also a single solid dot or single coordinate point at 1.2. So as you can see, we have what appears to be a linear part of our curve, and then what appears to be a parabolic shaped part of our curve, which is like shaped like a half a circle or a semicircle or an inverted upside down parabola. So now that we have a good visualization of what's happening in this particular prong, we can look that we can looking at our graph, we can say that from the graph, we can state that as X approaches -1 from the right. The function will approach a value of 1. So therefore we can go ahead and write that the limit as X approaches 1 from, so it's going to be as we once again, we need to note that the limit as X approaches -1. From the right, because once again, let me repeat, so looking at our graph, we could see that as X approaches -1 from the right, we can see that the function will approach a value of 1. So therefore, without a doubt, we can go ahead and write that the limit as X approaches -1 from the right, that's what that positive symbol in the power means, of F of X is going to be simply equal to 1. And because we just found out that the limit as X approaches -1 from the right of F of X equals 1, that means without a doubt. Our final answer has to be false because we just proved that the limit exists at 1. However, our statement says it's equal to 2, so that means our final answer has to be false. So without a doubt, our final answer has to be the letter B false. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Finding Limits Graphically

Which of the following statements about the function y = f(x) graphed here are true, and which are false?

j. limx→2− f(x) = 2

Key Concepts

Limits

One-Sided Limits

Graphical Interpretation of Limits

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