First we will calculate the vertical asymptote, is when the denominator of the function given is equal to zero
[tex]\begin{gathered} 2x+3=0 \\ x=-\frac{3}{2} \end{gathered}[/tex]
then we will calculate the horizontal asymptote because the degree of the numerator and the denominator is equal we can calculate the horizontal asymptote with the next operation
[tex]y=\frac{a}{b}[/tex]
a= the coefficient of the leading term of the numerator
b=the coefficient of the leading term of the denomintor
in our case
a=4
b=2
[tex]y=\frac{4}{2}=2[/tex][tex]y=2[/tex]
As we can see the graph that shown the asymptotes of the function is the graph in the option C.
