Solution:
\( \displaylines{x\text{-intercepts occur when }\left|3x+10\right|-2=0\implies\left|3x+10\right|=2\\ 3x+10=\pm2\implies3x=-10\pm2\\ 3x=-8\text{ or }3x=-12\\ x=-\frac83\text{ or }x=-4\\ \left(-\frac83,0\right)\text{ and }(-4,0)\\ \\ y\text{-intercept occurs when }x=0\implies y=\left|3\cdot0+10\right|-2=8\\ \left(0,8\right)\\ \text{Domain is all real numbers.}\\ \text{Range is }\left\lbrack-2,\infty\right)} \)