# How do you find the domain and range of #s(y) = (3y)/( y+5)#?

##### 1 Answer

Jun 25, 2017

#### Explanation:

The denominator cannot be zero as this would make the function undefined. Equating the denominator to zero and solving gives the value that y cannot be.

#"solve " y+5=0rArry=-5larrcolor(red)" excluded value"#

#rArr"domain " inRR,!=-5#

#"to find any excluded value in the range, we can find the"#

#"horizontal asymptote"#

#"divide terms on numerator/denominator by y"#

#((3y)/y)/(y/y+5/y)=3/(1+5/y)# as

#yto+-oo,s(y)to3/(1+0)#

#rArry=3larrcolor(red)" is an excluded value"#

#"range " inRR,y!=3#