The graph of the function has a vertical asymptote of x = The graph of the function has a horizontal asymptote of y = PLEASE ANSWER FAST
Accepted Solution
A:
The correct answers are: (1) The graph of the function has a vertical asymptote of x = 0
(2) The graph of the function has a horizontal asymptote of y = 0
Explanation: (1) To find the vertical asymptote, put the denominator of the rational function equals to zero.
Rational Function = f(x) = [tex] \frac{1}{x} [/tex]
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 = f(x) = [tex] \frac{1}{x} [/tex]
We can write it as:
f(x) = [tex] \frac{1 * x^0}{x^1} [/tex]
If power of x in numerator is less than the power of x in denomenator, then the horizontal asymptote will be y=0. If power of x in numerator is equal to the power of x in denomenator, then the horizontal asymptote will be y=(co-efficient in numerator)/(co-efficient in denomenator). If power of x in numerator is greater than the power of x in denomenator, then there will be no horizontal asymptote.
In above case, 0 < 1, therefore, the horizontal asymptote is y = 0