Question

What is the domain and range of:

Answer 1

$f(x)=\dfrac{2}{x+4}-7\\\\The\ domain:\\\\x+4\neq0\ \ \ |-4\\x\neq-4\to x\in\mathbb{R}-\{-4\}\to x\in(-\infty;\ -4)\ \cup\ (-4;\ \infty)$

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