Answer
$$
y=\frac{2x^{2}+3}{x^{2}+1}
$$
Has no vertical asymptotic line.
The line $y=2 $ is a horizontal asymptotic.
The y-intercept is 3.
This is graph $D$.
Work Step by Step
$$
y=\frac{2x^{2}+3}{x^{2}+1}
$$
has no vertical asymptotic line.
To find a horizontal asymptotic, let $x$ get larger and larger, so that $2x^{2}+3 \approx 2x^{2}$ because the 3 is very small compared with $2x^{2}$. Similarly, for $ x$ very large $x^{2}+1 \approx x^{2}$ . Therefore,
$$
y=\frac{2x^{2}+3}{x^{2}+1} \approx \frac{2x^{2}}{x^{2}} \approx 2.
$$
This means that the line $y=2 $ is a horizontal asymptotic.
When $x=0 $ the y-intercept is 3
This is graph $D$.
