Please help to explain!?

Question

Find the domain and the range of the function.

f(x) = (6/x+2) Please enter your answers in interval notation.

Find the range of the function. Find the domain of the function.

Answer 1

Rem y=f(x)= range

Need to graph some simple values of (x,y) by selecting say x=? then y=?, i.e., make an x,y table.



Notice x cannot = 0 if equation is (6/x)+2

or x cannot = -2 if equation is 6/(x+2)

Reason: can not divide by 0 since it is undefined.

So your domain is all numbers except 0 or -2.

Looking at the graph or equation it appears your range is all numbers.

Answer 2

Domain is what x can be.  Here as long as x isn't -2, which makes the bottom of the fraction be zero, it's fine.  So domain is ( -∞ , -2) U (-2, ∞)

Range is what the answer can come out.  If 6 is on top of the fraction then the fraction can never equal zero.  But any other number can be reached.  So the range is ( -∞ , 0) U (0, ∞)