Sketch the graph of a function with the given properties. You ...

Question

Sketch the graph of a function with the given properties. You do not need to find a formula for the function.

f(2) = 1,lim x→2 f(x) = 3

Accepted Answer

Welcome back, everyone. Identify the graph of the function with the given properties where F of 4 equals 5 and the limit of F of X as X approaches 4 equals 1. For our answer choices, we have the various graphs that we're going to look through to see which one of them satisfies the given conditions. So, let's start with the graph for answer choice A, OK? Now remember we're looking for a graph where FF 4 equals 5 and the limit of F of X as X approaches 4 equals 1. What do both of those things mean? Well, For our graph, notice it has a y and X axis, and we know. That Y is equal to FF X. So what F of 4 really means is that it's going to be the Y value on our graph where X equals 4. Now, when we look at our graph, is that value equal to 5? Well, when X equals 4, our graph here, the Y value, OK, if we come across, is going to be equal to 1, OK? Because notice here that our graph goes up by 2 units each time on the Y axis. So that means then for this graph, F of 4. is equal to 1. Now what about the limit of FX as X approaches 4? Well, as X approaches 4 from both sides, notice that the limit approaches 1. The FX the value of FX sorry approach is 1, OK? So the limit as X approaches 4 of FX also equals 1. Therefore, we know that this does not satisfy our conditions. Let's move on to answer choice B. No, for answer choice B, again, let's try to figure out what FF 4 is and also what the limit of FFX as X approaches 4 is, OK? Now, if we go here, notice that there's a solid dot when X equals 4 at Y equals 2. Therefore, F of 4 equals 2. And if we look at our function as it approaches from the left and from the right, notice that as X approaches 4, FF X sorry, FFX approaches 1, OK? Because that space, that blank spot, OK, if we come across, that's where our function is approaching and that is when FX equals 1. Though from these answer choices again we know that this does not satisfy the given properties. Let's move on to answer Try C. Now for answer to see, OK. First, again, we're looking for 44. And we're looking for the limit as X approaches 4 of above X, OK. And now, starting with F of 4, OK, when X equals 4, right? Not that our graph or value here for F of X or, or, or red curve here is going to be equal to 1, OK? So notice that it equals 1. So F of 4 E equals 1, and if we look at the limit of FX as X approaches 4 from both sides, notice that FX also approaches 1. So again, C is not the correct answer. Now what about answer choice D? Well, no, when we look at answer twiceD, OK, so FFX, uh, sorry, FF 4. And the limit of F of X as X approaches 4, starting with F of 4, OK. When X equals 4, OK. Not that we have a solid dot when, OK, we have a solid do when X equals, sorry, when Y equals 5. So F of 4 equals 5. As for the limit, when we look at our limit as X, X approaches 4 from both sides, notice that our limit, OK, approaches this empty space here which corresponds to 1 on the Y axis. So the limit of FF X as X approaches 4 equals 1. This is the property, these are the properties, sorry, that we mentioned earlier. Therefore, that tells us D is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

Sketch the graph of a function with the given properties. You do not need to find a formula for the function.

f(2) = 1,lim x→2 f(x) = 3

Key Concepts

Function Value

Limit

Graphical Representation

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