Question

In Exercise,find the horizontal asymptote of the graph of the function.
f(x) = 3/2+(1/x)

Answer 1

`y=(3)/(2)`

Explanation:

We are given that a function

`f(x)=(3)/(2+(1)/(x))`

We have to find the horizontal asymptote of the graph of the function.

The given function can be written as

`f(x)=(3)/((2x+1)/(x))`

`f(x)=(3x)/(2x+1)`

Degree of polynomial of numerator=1

Degree of polynomial of denominator=1

Degree of numerator=Degree of denominator

When degree of denominator is equal to degree of numerator then horizontal asymptote is equal to quotient obtained by dividing the coefficient of highest power of x in numerator with coefficient of highest power of x in denominator.

Therefore, horizontal asymptote=
`(3)/(2)`