Question Video: Finding the One-Sided Limit of a Function from Its Graph | Nagwa Question Video: Finding the One-Sided Limit of a Function from Its Graph | Nagwa

# Question Video: Finding the One-Sided Limit of a Function from Its Graph Mathematics • Second Year of Secondary School

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Use the graph below to find lim_(π₯ β 5βΊ) π(π₯).

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### Video Transcript

Use the graph below to find the limit as π₯ approaches five from the right of π of π₯.

Weβre given a graph of the function π of π₯. We need to use this graph to determine the limit as π₯ approaches five from the right of π of π₯. To do this, letβs start by recalling what we mean by the limit as π₯ approaches five from the right of a function π of π₯. This is equal to the value π of π₯ approaches as π₯ tends to five where π₯ must be greater than five. In other words, as our input values of π₯ approach the value of five from the right, we want to know what happens to our output values of π of π₯.

We can do this by using our graph. We know that our input values of π₯ will be on the π₯-axis. So letβs mark π₯ is equal to five. We might be worried from our sketch that when we input π₯ is equal to five, we can see that π of π₯ is undefined. This is represented by the hollow circle. But remember, weβre only seeing what happens to our outputs as π₯ approaches five. And in this case, π₯ must be greater than five. π₯ is never equal to five.

So letβs see what happens to our outputs of π of π₯ as π₯ approaches five from the right. First, we can see that our function π of π₯ is not defined when π₯ is greater than eight. So we should pick inputs smaller than this. Letβs start with π₯ is equal to seven. From our diagram, we can find the output of π of π₯ when π₯ is equal to seven. We get π of seven is equal to negative six. We can do the same when π₯ is equal to six. We see that π of six is also equal to negative six.

In fact, we can see exactly the same thing happens as our values of π₯ approach five from the right. They always output negative six. And if our outputs are remaining constant at negative six, we can also say theyβre approaching negative six. Therefore, weβve shown as π₯ approaches five from the right, π of π₯ approaches negative six. Or, in other words, the limit as π₯ approaches five from the right of π of π₯ is equal to negative six.

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