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

1 Answer
Jul 1, 2017

Answer:

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.