Question

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What are the coordinates of the hole in the graph of the function?

f(x)=x2−3x−10/x−5
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Answer 1

(5, 7)

Explanation:

A hole is found in the graph of a rational function where numerator and denominator factors cancel each other.

The x-coordinate of the hole is the value of x that makes the factor zero. The y-coordinate of the hole is the value of the simplified function after the cancelled factors are removed. It is the limit of the function value as x approaches the hole location.

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`f(x)=(x^2-3x-10)/(x-5)=((x+2)(x-5))/(x-5)=x+2\qquad x\\e 5`

The hole is found at x = 5. The limit of the function value as x approaches 5 is 5+2 = 7. The coordinates of the hole are (5, 7).