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?

d. limx→1− f(x) = 2

Accepted Answer

Hello there. Today we're gonna 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 validity of the following statement based on the given graph of Y equals F of X. The limit as X approaches -1 from the left of F of X is equal to -1. Awesome. So it appears for this particular problem we're trying to take our given statement, which once again is the limit as x approaches -1 from the left of F of X is equal to -1, and we're trying to prove whether or not this statement is either a true or B false based on our given graph of Y equals F of X. So with that said, let's quickly look at our graph to see what exactly is happening to help us better visualize what's going on. And as we can see, we, what appears to be two separate curves, but technically it's the same curve, and the reason why it's the same curve is because we have a hole or a discontinuity. And what happens here is the curve disappears into the hole and then it reappears at another point in the graph and then continues. So with that said, we have two different parts of our curve. We have a linear part of our curve, and then we have another part of our curve, which is shaped like a fin on a fish or like a dolphin or a shark or maybe even a wave. It's like shaped like that. And we also have a linear shaped curve, so our linear part of the curve, so a linear shaped part of our curve. So it starts at -3-1 at a solid point, and then it leads to a hole at -2.1, and then continues further to a solid point at -11. We also have a solid point all by itself at -22. We also have another hole at 0.1, and then it goes up to touch the Y axis at 0.2, and then it curves down to touch the X axis at 0.2. Fantastic. So now that we have a good visualization of what's happening in this particular prompt, let us note that from the graph as X approaches -1 from the left, the function will approach a value of -1. Therefore, we go ahead and write that the limit as X approaches. -1 from the left of F of X, we could say that this is equal to -1, and because we just proved this particular statement, that will mean that our statement that's given to us in the problem itself, which once again the limit as X approaches -1 from the left. F of X is equal to -1. That means that we just proved our statement is true, so that means our final answer has to be the letter A true. 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?

d. limx→1− f(x) = 2

Key Concepts

Limits

One-Sided Limits

Graphical Interpretation of Limits

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