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For what value(s) of x does the graph of g(x) = x+10/x^3+5x^2-50x have a hole?

 

 Apr 13, 2020
 #1
avatar+23689 
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Anywhere the denominator = 0   there will be a hole

x=0    produces a denominator = 0      so that is one hole....

    now you try x= 10     and -10    to see if denominator = 0   ,    another hole

 Apr 13, 2020
 #2
avatar+21004 
+1

Factor (if necessary) both the numerator and the denominator of the function.

 

If you have a term in the numerator which cancels a term in the denominator, then there will be a hole where 

this term becomes zero.

 

For instance, if the function is:  f(x)  =  [ (x + 6)(x - 9) ] / [ (x + 7)(x - 9) ]

there will be a hole at x = 9 and the function reduces to  f(x)  =  (x + 6) / (x + 7).

 

There won't be a hole at x = -7; here, expect a vertical asymptote.

 Apr 13, 2020

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