$\left(2,0\right)$ 

 $\left(3,0\right)$ 

No Hole

$x=-\frac{1}{5}$

$y=0$

$y=1$

No Horizontal Asymptote

 $x=0$ 

 $x=-3$ 

No Vertical Asymptote

 $x=2$  

 $\left(0,\frac{7}{3}\right)$ 

 $\left(-3,0\right)$ 

No Hole

 $\left(2,\frac{9}{5}\right)$  

$y=0$

$y=3$

No Horizontal Asymptote

0

1

2

$x=3$

$x=-1$

No Hole

$x=3$

$x=-1$

No Vertical Asymptote

 $x=0$  

Yes Vertical, No Horizontal

Yes Vertical, Yes Horizontal

No Vertical, No Horizontal

No Vertical, Yes Horizontal

$\left(4,8\right)$

$\left(0,4\right)$

$\left(-4,8\right)$

$x=4,\ x=-2$

$x=4$

$x=-2$

greater than

less than

equal to

$f\left(x\right)=\frac{x-4}{x+3}$

$f\left(x\right)=\frac{x+2}{x-4}$

$f\left(x\right)=\frac{x+2}{x+3}$

$f\left(x\right)=\frac{x-3}{x+2}$

 $y=0$ 

 $y=1$ 

 $None$ 

None

1

2

$x=-4,\ x=4$

$x=1,\ x=4$

Vertical

Horizontal

Oblique