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?

e. limx→1+ f(x) = 1

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 validity of the following statement based on the given graph of Y equals F of X. The limit as X approaches -1 from the right of F of X is equal to 0. So it appears for this particular problem we're asked to take our given statement, which once again is the limit as X approaches -1 from the right of F of X equals 0, and we're trying to determine whether or not the statement is a true or B false, based on our given. Graph of Y equals F of X. So with that said, now that we know what we're trying to solve for, let's look at our graph that is provided to us. And as we look at our graph, we could see what appears to be two separate curves, but technically they're the same curve, and the reason why is because as you can see. We have a few discontinuities in our curve, which are represented by these holes, which are white dots with a black ring around them. And as you can see, the curve goes from a solid point, which is at 0.2, and then it goes up to touch our Y axis, which is like a fin shape or like a dolphin fin shark fin shape, and it goes up to touch our Y axis at 0.2. So once again, it starts at 2.0, then it curves up to 0.2, and then it dips down. To our whole, which is at -1.0. And then we have our linear part of our graph, which starts at a solid point at -3.1, then goes to a hole at -2.1, and then it goes to a solid point at -1.1. And then we also have another solid point all by itself at -2.2. And once again, our curve is represented in red for Y equals F of X. So now that we have a good visualization of what's happening in this particular prompt, let us note that from the graph itself as X approaches -1 from the right, the function will approach a value of 0. So it will approach a value of 0. So therefore we can go ahead and write that the limit. As x approaches -1 from the right of F of X is equal to 0, and because we just proved this statement, we can go ahead and look at our given statement, which once again is the limit as X approaches -1 from the right of F of X is equal to 0, and we just proved that statement to be true. So that means without a doubt, our final answer has to be 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?

e. limx→1+ f(x) = 1

Key Concepts

Limits

One-Sided Limits

Graphical Interpretation of Limits

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