Question

Find the coordinate point of the hole in the function below

Answer 1

(6, 2/7)

Explanation:

You want the coordinates of the hole in the graph of (n² -10n +24)/(n² -5n -6).

Simplify

Simplifying the given rational expression, we have ...

`(n^2-10n+24)/(n^2-5n-6)=((n-6)(n-4))/((n-6)(n+1))=(n-4)/(n+1)\quad n\\e6`

At n = 6, the simplified expression is ...

(6 -4)/(6 +1) = 2/7

The hole is located at (6, 2/7).

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Additional comment

Even though the factor (n-6) in the denominator cancels the one in the numerator, the function remains undefined there. Hence the "hole". If there were no corresponding numerator factor at that point, there would be another vertical asymptote at n=6.

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