# Thread: now how do i find the aymptotes?

1. ## now how do i find the aymptotes?

$3^{x+2}-1$

How do I find the asymptotes of this (vertical, horizontal)?

2. let f(x) = 3^x
this graph has f(x) > 0

then 3^(x+2) -1

is a transformation on f(x)
so:

f(x+2) - 1

this is a vertical translation of -1 and a horizontal translation of left 2 units

we care only about the vertical translation
now we have f(x) > -1

so the horizontal asymptote is y = -1
since the curve approaches -1 when x is large negative

3. Hi
How do I find the asymptotes of this (vertical, horizontal)?
Vertical asymptotes exist where the function is not defined : at the boundaries of its domain, each time that $\lim_{x\to x_0}f(x)=\pm\infty$, $x=x_0$ is a vertical asymptote for the curve.
Horizontal ones exist when the function has a limit when $x$ approaches $\pm\infty$. (for example $y=0$ is an horizontal asymptote as $x$ approaches both $-\infty$ and $\infty$ for $x\mapsto\frac{1}{x}$)