# How do you find the domain and range of f(x)=(2x-3)/(x+2)?

Jul 1, 2017

See below

#### Explanation:

The domain is all the values that $x$ is allowed to take on. The only problem I have with this function is that I need to be careful not to divide by zero. So the only values that x can not take on are those which would cause division by zero. So I'll set the denominator equal to zero and solve; my domain will be everything else.

$x + 2 = 0$
$x = - 2$

So the domain of this function is everything from positive infinity to negative infinity except $- 2$.

The range is all the values that $y$ will take on. In this case, the range is all x.