$f\left(x\right)=\frac{1}{x-1}-1$

$f\left(x\right)=\frac{1}{x+1}+1$

$f\left(x\right)=\frac{1}{x-1}+1$

$f\left(x\right)=-\frac{1}{x-1}+1$

$f\left(x\right)=\frac{1}{x+2}-3$

$f\left(x\right)=\frac{1}{x+2}+3$

$f\left(x\right)=\frac{1}{x-3}+2$

$f\left(x\right)=\frac{1}{x+3}-2$

$f\left(x\right)=\frac{1}{x-1{,}5}+2$

$f\left(x\right)=\frac{3}{x-1{,}5}+2$

$f\left(x\right)=\frac{1}{x+1{,}5}+2$

$f\left(x\right)=\frac{3}{x-2}+1{,}5$