What is the domain and range of  y=3/(x+4)?

Apr 27, 2017

$x \in \mathbb{R} , x \ne - 4$

$y \in \mathbb{R} , y \ne 0$

Explanation:

The denominator of y cannot be zero as this would make y $\textcolor{b l u e}{\text{undefined}} .$ Equating the denominator to zero and solving gives the value that x cannot be.

$\text{solve " x+4=0rArrx=-4larrcolor(red)" excluded value}$

$\Rightarrow \text{domain is } x \in \mathbb{R} , x \ne - 4$

$\text{to find range express function with x as subject}$

$\Rightarrow y \left(x + 4\right) = 3$

$\Rightarrow x y + 4 y = 3$

$\Rightarrow x y = 3 - 4 y$

$\Rightarrow x = \frac{3 - 4 y}{y}$

$\text{the denominator cannot be zero}$

$\Rightarrow \text{range is } y \in \mathbb{R} , y \ne 0$
graph{3/(x+4) [-16.02, 16.02, -8.01, 8.01]}