(a) – A, because this function has $textbf{a vertical asymptote at}$ $x=3$;

(b) – C, because this function has $textbf{a hole at}$ $x=3$;

(c) – F, because this is reciprocal quadriatic function and it has $textbf{a vertical asymptote at}$ $x=3$;

(d) – D, because this function has $textbf{vertical asymptotes at}$ $x=1$ and $x=-3$;

(e) – B, because this function $textbf{has no zeros.}$;

(f) – E, it has an oblique asymptote because the degree of $p(x)=x^2$ is greater than $q(x)=x-3$ by exactly $1$.

#### (a)

This function has $textbf{vertical asymptote at}$ $x=-4$ and $textbf{horizontal asymptote at}$ $y=1$.
#### (b)

This function has $textbf{vertical asymptote at}$ $x=-dfrac{3}{2}$.
#### (c)

This function has $textbf{vertical asymptote at}$ $x=6$ and $textbf{horizontal asymptote at}$ $y=2$.
#### (d)

This function has $textbf{a hole at}$ $x=-3$.
#### (e)

This function has $textbf{vertical asymptotes at}$ $x=-3$ and $x=5$.
#### (f)

This function has $textbf{vertical asymptote at}$ $x=-1$ and $textbf{horizontal asymptote at}$ $y=-1$.
#### (g)

This function has $textbf{a hole at}$ $x=2$.
#### (h)

This function has $textbf{vertical asymptote at}$ $x=dfrac{5}{2}$ and $textbf{horizontal asymptote at}$ $y=-2$.
#### (i)

This function has $textbf{vertical asymptote at}$ $x=-dfrac{1}{4}$ and $textbf{horizontal asymptote at}$ $y=2$.

#### (j)

This function has $textbf{a hole at}$ $x=-4$ and $textbf{vertical asymptote at}$ $x=4$.
#### (k)

This function has $textbf{vertical asymptote at}$ $x=dfrac{3}{5}$ and $textbf{horizontal asymptote at}$ $y=dfrac{1}{5}$.
#### (l)

This function has $textbf{vertical asymptote at}$ $x=4$ and $textbf{horizontal asymptote at}$ $y=-dfrac{3}{2}$.

#### (a)

This might be function:

$$
f(x)=dfrac{x-1}{x^2-1}
$$

#### (b)

This might be function:

$$
f(x)=dfrac{1}{x-2}
$$

#### (c)

This might be function:

$$
f(x)=dfrac{x+2}{(x+2)(x-1)}
$$

#### (d)

This might be function:

$$
f(x)=dfrac{2x}{x+1}
$$

#### (e)

This might be function:

$$
f(x)=dfrac{x^2+3}{x+2}
$$

(a) $f(x)=dfrac{x-1}{x^2-1}$; (b) $f(x)=dfrac{1}{x-2}$; (c) $f(x)=dfrac{x+2}{(x+2)()x-1}$; (d) $f(x)=dfrac{2x}{x+1}$; (e) $f(x)=dfrac{x^2+3}{x+2}$;