Question

How do you find the asymptotes for `y= (x + 2) /( x + 3)`?

Answer 1

Vertical Asymptote: `x=-3`
Horizontal asymptote: `y=1`

Explanation:

To find the vertical asymptote take the denominator and set it equal to zero and solve for x. To find the horizontal asymptote use the end behavior method i.e take the highest degree term from the top and divide by the highest degree term from the bottom and then simplify.

Answer 2

vertical asymptote x = -3
horizontal asymptote y = 1

Explanation:

Vertical asymptotes occur as the denominator of a rational function tends to zero. To find the equation equate the denominator to zero.

solve x + 3 = 0 → x = - 3 is the equation

Horizontal asymptotes occur as `lim_(x→±∞) f(x) → 0`

If the degree of the numerator and denominator are equal, as in this case both of degree 1. The equation can be found by taking the ratio of leading coefficients.

`y = 1/1 = 1 rArr y = 1 " is the equation "`

Here is the graph of the function.
graph{(x+2)/(x+3) [-10, 10, -5, 5]}