$a)f\left(-3\right)=3\cdot \left(-3\right)+1=-9+1=-8$  

$f\left(-1\right)=3\cdot \left(-1\right)+1=-3+1=-2$  

$f\left(0\right)=3\cdot 0+1=1$  

$f\left(5\right)=3\cdot 5+1=15+1=16$ $f\left(5\right)=3\cdot 5+1=15+1=16$  

$Z_w=\left\{-8,-2,1,16\right\}$  

 

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

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

$f\left(0\right)=\frac{0}{0+2}=\frac{0}{2}=0$  

$Z_w=\left\{-1,0,\frac{1}{5}\right\}$  

 

$c)f\left(0\right)=0\sqrt{0}=0$  

$f\left(1\right)=1\cdot \sqrt{1}=1$  

$f\left(4\right)=4\cdot \sqrt{4}=4\cdot 2=8$  

$Z_w=\left\{0,1,8\right\}$  

 

$d)f\left(-2\right)={\left(-2\right)}^4=16$  

$f\left(-1\right)={\left(-1\right)}^4=1$  

$f\left(0\right)=0^4=0$  

$f\left(1\right)=1^4=1$  

$Z_w=\left\{0,1,16\right\}$