Find the following limits and identify the horizontal asymptotes (if any) for the function $g\left(x\right)=\frac{4x^2+5x-3}{2x^2-7}$:
$\lim_{x\rightarrow\infty}g\left(x\right)$
$\lim_{x\rightarrow-\infty}g\left(x\right)$

$\lim_{x\rightarrow\infty}g\left(x\right)$ $=\frac12$

$\lim_{x\rightarrow-\infty}g\left(x\right)$ $=-\frac12$

Horizontal asymptotes: $y=2$ and $y=-2$

$\lim_{x\rightarrow\infty}g\left(x\right)=2$

$\lim_{x\rightarrow-\infty}g\left(x\right)=2$

Horizontal asymptote: $y=2$

$\lim_{x\rightarrow\infty}g\left(x\right)$ $=1$

$\lim_{x\rightarrow-\infty}g\left(x\right)$ $=1$

Horizontal asymptote: $y=-1$

$\lim_{x\rightarrow\infty}g\left(x\right)$ $=1$

$\lim_{x\rightarrow-\infty}g\left(x\right)$ $=-1$

No horizontal asymptote