Answer:
The correct answers are:
(1) The vertical asymptote is x = 0
(2) The horizontal asymptote is y = 0
Explanation:
(1) To find the vertical asymptote, put the denominator of the rational function equals to zero.
Rational Function = g(x) =
Denominator = x = 0
Hence the vertical asymptote is x = 0.
(2) To find the horizontal asymptote, check the power of x in numerator against the power of x in denominator as follows:
Given function = g(x) =
We can write it as:
g(x) =
If power of x in numerator is less than the power of x in denominator, then the horizontal asymptote will be y=0.
If power of x in numerator is equal to the power of x in denominator, then the horizontal asymptote will be y=(co-efficient in numerator)/(co-efficient in denominator).
If power of x in numerator is greater than the power of x in denominator, then there will be no horizontal asymptote.
In above case, 0 < 1, therefore, the horizontal asymptote is y =