Calculate the poles of a function - this is how it works

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Finding the pole position is an almost impossible task for many people. But with a little practice and the necessary know-how, you too will surely achieve the desired result.

Arithmetic can also be fun.
Arithmetic can also be fun.

What you need poles for

  • When one speaks of poles, one speaks of the behavior x towards infinity or x towards minus infinity.
  • This is mostly used to describe and interpret graphs and their behavior.

How to correctly determine the poles

  1. For example, if you use the function f (x) = x3 - 9x2 + 24x -16, we know that x3-Functions usually have a waveform. D. H. it either comes from below and goes up, or it comes from above and goes down.
  2. If the function comes from below and runs upwards, then the functions x runs towards minus infinity also towards x towards minus infinity. For x towards plus infinity, the function would then also go towards plus infinity.
  3. To find out the case in this task, it is enough to look at the highest potency. That would then be x3.
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  4. In order to find out x towards minus infinity, you have to look for a value that is as small as possible, because all axes of a coordinate system are there go towards infinity, one wants to find a number for the case x towards minus infinity that is as far to the left as possible on the coordinate system. For example, you could take -1000.
  5. Put e.g. B. for the power x3 -1000 a. D. H. They would have (-1000)3. This would result in -100,000,000,000. You can see that the minus remains. This shows that the function goes down, i.e. the function f (x) goes towards minus infinity.
  6. For the second case, i.e. x towards plus infinity, one looks whether the graph goes very far down or very far up on the right side of the coordinate system. To do this, insert as large a value as possible, e.g. B. 1000. You put this in x again3 one, so 10003which is 1000000000. The value remains positive, which means that f (x) tends towards plus infinity.

You don't have to pay more attention to anything else when determining pole positions.

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