What is the domain and range of #y = (x + 3) / (x -5)#?

1 Answer
Mar 17, 2018

Answer:

Domain: #(-oo,5)uu(5,oo)#
Range: #(-oo,1)uu(1,oo)#

Explanation:

Ok, lets start with the Domain
The domain of this equation is all numbers except when you divide by #0#. So we need to find out at what #x# values does the denominator is equal to #0#. To do this we simply we the denominator equal to #0#. Which is

#x-5=0#

Now we get #x# alone by adding #5# is both sides, giving us
#x=5#

So at #x=5# this function is undefined.
That means that every other number you can think of will be valid for this function. Which gives us #(-oo,5)uu(5,oo)#

Now to find the Range
The range can be found by dividing the leading coefficients from the numerator and the denominator. In the numerator we have #x+3# and in the denominator we have #x-5#

Since there is no number in front of the #x# values we just treat it as #1#

So it would #1/1# which is #1#.
So the range is #(-oo,1)uu(1,oo)#