Question

What is the domain and range of:

Answer 1

`f(x)=(2)/(x+4)-7\\\\The\ domain:\\\\x+4\\eq0\ \ \ |-4\\x\\eq-4\to x\in\mathbb{R}-\{-4\}\to x\in(-\infty;\ -4)\ \cup\ (-4;\ \infty)`

`The\ range\ of\ function\ y=(a)/(x)\ is\ equal\ \mathbb{R}-\{0\},\ therefore\\\\the\ range\ of\ y=(2)/(x+4)\ is\ equal\ \mathbb{R}-\{0\}=(-\infty;\ 0)\ \cup\ (0;\ \infty).\\\\We\ have\ f(x)=(2)/(x+4)-7,\ therefore\ the\ graph\ of\ function\\\\y=(2)/(x+4)\ we\ move\ 7\ units\ down.\\\\Therefore\ the\ range\ is\ equal\ \mathbb{R}-\{-7\}=(-\infty;\ -7)\ \cup\ (-7;\ \infty)`