Question

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

Answer 1

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.