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What are the coordinates of the hole in the graph of the function f(x) ?

 

f(x) = x^2 − 9 / x − 3

 

(I think its [3,6] because that's where it becomes 'undefined'. Am I wrong? Please let me know, I appreciate it).

 Feb 28, 2019

Best Answer 

 #1
avatar+17275 
+2

The hole in the graph occurs when the denominator = 0   (undefined point)

    this occurs at x = 3

 

The NUMERATOR factors in to  (x-3)(x+3)     this reduces to  (x+3) when you 'cancel out' with the denominator (x-3)

     this value at x = 3          is (x+3) = 6

so the point of the hole is    3,6

 Feb 28, 2019
 #1
avatar+17275 
+2
Best Answer

The hole in the graph occurs when the denominator = 0   (undefined point)

    this occurs at x = 3

 

The NUMERATOR factors in to  (x-3)(x+3)     this reduces to  (x+3) when you 'cancel out' with the denominator (x-3)

     this value at x = 3          is (x+3) = 6

so the point of the hole is    3,6

ElectricPavlov Feb 28, 2019

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