# Question Video: Finding the Limit of a Function from Its Graph Mathematics • 12th Grade

Using the graph representing the function π(π₯) = (π₯ + 3)Β² + 2, determine lim_(π₯ β β3) π(x).

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### Video Transcript

Using the graph representing the function π of π₯ is equal to π₯ plus three all squared plus two, determine the limit as π₯ approaches negative three of π of π₯.

Weβre given a graph, and weβre told that the curve in this graph represents the function π of π₯ is equal to π₯ plus three all squared plus two. We need to use this graph to determine the value of the limit as π₯ approaches negative three of the function π of π₯. First, letβs recall what we mean by the limit as π₯ approaches negative three of the function π of π₯. This is the value that our outputs of π of π₯ approach as π₯ tends to negative three. In other words, we want to see what happens to the outputs of π of π₯ as our inputs π₯ get closer and closer to negative three. So letβs mark negative three on our π₯-axis. Remember, the outputs of our function will be their π¦-coordinate.

We now want to see the value π of π₯ approaches as π₯ tends to negative three. Letβs start by looking at what happens as our values of π₯ approach negative three from the left. As our values of π₯ approach negative three from the left, we can see something interesting. By remembering that our outputs are represented by the π¦-coordinate, we can see this is approaching two. But we can then ask the question, what happens as our values of π₯ approach negative three from the right? This means our values of π₯ will be bigger than negative three. We can see we get a very similar story. As our values of π₯ approach negative three from the right, our outputs are still getting closer and closer to two. So as our values of π₯ are getting closer and closer to negative three, our outputs π of π₯ are getting closer to two.

Therefore, by using the graph representing the function π of π₯ is equal to π₯ plus three all squared plus two, we were able to show the limit as π₯ approaches negative three of π of π₯ is equal to two.