[tex]f(x)=\dfrac{1}{3x+2}\to y=\dfrac{1}{3x+2}\\\\\text{exchange x to y}\\\\x=\dfrac{1}{3y+2}\qquad\text{solve for y}\\\\\dfrac{1}{3y+2}=x\qquad\text{multiply both sides by}\ 3y+2\neq0\\\\1=x(3y+2)\qquad\text{divide both sides by }\ x\neq0\\\\\dfrac{1}{x}=3y+2\qquad\text{subtract 2 from both sides}\\\\\dfrac{1}{x}-2=3y\qquad\text{divide both sides by 3}\\\\\dfrac{1}{3x}-\dfrac{2}{3}=y\to y=\dfrac{1}{3x}-\dfrac{2}{3}[/tex]
[tex]Domain:\ 3x\neq0\to x\neq0\\Vetical\ asyptote:y=-\dfrac{2}{3}\\\\Answer:\\domain\ (-\infty,\ 0)\ \cup\ (0,\ \infty)\\\\range\ \left(-\infty,\ -\dfrac{2}{3}\right)\ \cup\ \left(-\dfrac{2}{3},\ \infty\right)[/tex]
