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

1 Answer
MG
May 3, 2018

Domain: #x!=3#
Range: #y!=3#

Explanation:

the denominator cannot equal zero, as this is where the function is undefined. #x=3# will make the denominator zero, therefore this value is not part of the domain, in fact the line #x=3# becomes a vertical asymptote, meaning the graph on either side of this line never touches it. The Domain is the set of all real #x# values that DEFINE the function. The range is the set of all real #y# values that correspond with the domain. The line #y=3# is a horizontal asymptote. graph{(3x+2)/(x-3) [-25.66, 25.65, -13.37, 13.37]}

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