Given this function: f(x) =3/[x+3] -9

explain how you'd identify the vertical asymptote of the function **without graphing**.

identify the horizontal asymptote of the function writing the entire equation

also can you explain how to identify the horizontal asymptote of the function without graphing.

jj88778 Feb 19, 2019

#1**+3 **

f(x) = 3 / { x + 3] - 9

The vertical asymptote is the value of x that makes the denominator = 0

So....

x + 3 = 0

x = - 3 ⇒ vertical asymptote

To find the horizontal asymptote.....note that 3/ [ x +3 ] is a lower power polynomial / higher power polynomial

When we have this situation, the horizontal asymptote is y = 0

* However .....* the "-9" at the end actually shifts this horizontal aymptote DOWN by 9 units

So....the horizontal asymptote is y = - 9

Here's the graph : https://www.desmos.com/calculator/93af4udovt

CPhill Feb 19, 2019