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

Question

2529 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-05-10T16:44:44

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 $x->+-oo$ .

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