Answer:
[tex]y=\frac{3}{2}[/tex]
Step-by-step explanation:
We are given that a function
[tex]f(x)=\frac{3}{2+\frac{1}{x}}[/tex]
We have to find the horizontal asymptote of the graph of the function.
The given function can be written as
[tex]f(x)=\frac{3}{\frac{2x+1}{x}}[/tex]
[tex]f(x)=\frac{3x}{2x+1}[/tex]
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=[tex]\frac{3}{2}[/tex]
