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

1 Answer
Jim G.
Jun 25, 2017

#"domain "inRR,!=-5#
#"range "inRR,!=3#

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#

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