Question

How do you find the end behavior of `y = (2x+3) /( x+2)`?

Answer 1

The dominant terms in the numerator and denominator as `x -> +-oo`, will be the ones in `2x` and `x` respectively.

The limit of `(2x)/x` as `x->oo or -oo` is 2.

More formally, we have

`y = (2x+3)/(x+2) = (2x+4-1)/(x+2) = (2(x+2)-1)/(x+2)`

`= 2(x+2)/(x+2)-1/(x+2) = 2-1/(x+2)`

The term `1/(x+2)->0` as `x->+-oo`.