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

Guest Apr 13, 2020

#1**+1 **

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

ElectricPavlov Apr 13, 2020

#2**+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.

geno3141 Apr 13, 2020