# Question Video: Finding the Limit of a Function from Its Graph If the Limit Exists Mathematics

Determine the limit as π₯ βΆ 2 of the function represented by the graph.

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### Video Transcript

Determine the limit as π₯ tends to two of the function represented by the graph.

Now, if we look at the graph, we can see that the function is called π of π₯. And weβve being asked to find the limit of π of π₯ as π₯ tends to two. In other words, this is the limit as π₯ tends to two of π of π₯. This can also be described as the value π of π₯ approaches as π₯ tends to two. So we need to find this value of π of π₯ using our graph. We can consider what π of π₯ is doing around the value of π₯ is equal to two. Weβll need to consider π of π₯ on both the left and right of two. Letβs consider π of π₯ on the right of π₯ is equal to two. We can see that as π₯ gets closer and closer to two, π of π₯ is decreasing. And it is decreasing towards this point here, which has a value of three. So we can say that as π₯ tends to two from the right, the value of π of π₯ approaches three.

Letβs now consider what happens on the left of π₯ is equal to two. We can again see that as π₯ gets closer and closer to two, the value of π of π₯ is decreasing. And from the graph, we can see that it is decreasing towards the same value that π of π₯ is approaching from the right as π₯ approaches two. And thatβs a value of three. So now we can say that as π₯ approaches two from the left, π of π₯ approaches three. Since π of π₯ approaches the same value from the left and the right of two, we can therefore conclude that the value that π of π₯ approaches as π₯ tends to two is three. And so, we reach our solution, which is that the limit as π₯ approaches two of π of π₯ is equal to three.