Thread: Are asymptotes effected by vertical/horizontal expansion or compression??

as the question says, are the graphs effected.... the basic equation is so if it'z like will the resulting graph be different than

The asymotopes wnt be affected, in that example by compression and expansion as the asymotopes lie on the x and y axis, the general steepness of the graph will increase tho.

Originally Posted by chris_uk

The asymotopes wnt be affected, in that example by compression and expansion as the asymotopes lie on the x and y axis, the general steepness of the graph will increase tho.

will it stay the same if i add horizontal and vertical shifts 2 it..

If you added a shift to it the expansion or compression would affect the asymotopes just as it would any other point
e.g.
if you had y=1/x +2 where the asymotopes are at y=2 and x=0

a vertical expansion of scale factor 2... y=2(1/x +2) can be written as y=2/x +4. Where the asymotopes are y=4 and x=0
note: y=1/x +1 is not equal to y=1/(x+1) it wasn't very clear wen i wrote it.

Originally Posted by ruscutie100

will it stay the same if i add horizontal and vertical shifts 2 it..

If you have , the vertical and horizontal asymptotes are obviously not changed by a dilation from either axis.

But consider , say. This can be got by applying appropriate translations to f(x). g(x) has a vertical asymptote x = 1 and a horizontal asymptote y = 2. (So applying translations to will change its asymptotes, if that's what you were asking).

But if you want to know whether dilations will have an affect on asymptotes after translations have been added to , then consider:

Dilation by factor a from horizontal axis: . Clearly .

h(x) still has a vertical asymptote x = 1 but the horizontal asymptote is y = 2a.

Dilation by factor 1/a from vertical axis: . Clearly .

k(x) now has a vertical asymptote x = 1/a and the horizontal asymptote is still y = 2.