SOLUTION: 2/(x-2)*2
1. what is the vertical asymptote
2. horizontal symptoto
3. what are the zeros if any ?
Algebra.Com
Question 203165: 2/(x-2)*2
1. what is the vertical asymptote
2. horizontal symptoto
3. what are the zeros if any ?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
There is a vertical asymptote at 
where 
is any value that would make the denominator zero, provided that it doesn't make the numerator zero also.
Compare the degree of the numerator polynomial to the degree of the denominator polynomial. If the degree of the denominator is greater than the degree of the numerator, then there is a horizontal asymptote at 
. If the degree of the numerator and denominator are the same, then there is a horizontal asymptote at 
where is the lead coefficient of the numerator and 
is the lead coefficient of the denominator. If the degree of the numerator is larger than the degree of the denominator by 1 then there is an oblique asymptote whose equation is the quotient excluding any remainder obtained by performing polynomial long division of the numerator by the denominator.
In order for a rational expression to be equal to zero, there must be a value of the variable that makes the numerator equal to zero. So to answer your question, you must ask yourself "Is there any value of the variable that will cause 2 to be equal to zero?" If there are, then those values are the zeros of the rational expression. If not, then there are no zeros.
John
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