Question

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

Answer 1

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]}