$\displaystyle 3^{x+2}-1$

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

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- Apr 27th 2008, 12:16 PMtheevilp0ptartnow how do i find the aymptotes?
$\displaystyle 3^{x+2}-1$

How do I find the asymptotes of this (vertical, horizontal)? - Apr 27th 2008, 12:38 PMfinch41
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 - Apr 27th 2008, 12:41 PMflyingsquirrel
Hi

Quote:

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

Horizontal ones exist when the function has a limit when $\displaystyle x$ approaches $\displaystyle \pm\infty$. (for example $\displaystyle y=0$ is an horizontal asymptote as $\displaystyle x$ approaches both $\displaystyle -\infty$ and $\displaystyle \infty$ for $\displaystyle x\mapsto\frac{1}{x}$)