Question

Do e functions such as (1/2)e^(-x^(2) +2) + 1 have asymptotes?

Answer 1

the engine room of this function is the exp(-x^2) or 1/exp(x^2)

clearly symmetrical about the y axis as the x is squared and clearly tending to but never reaching zero as x -> + or - infinity, meaning i guess that the x-axis in my simplified example is an asymptote.

on the chart the red line is my simplified function, the blue line is your function which show how the extra bits you have added just move and scale.

i hope this is of some help.

Answer 2

so the horizontal asymptote is y = 1?

Answer 3

i thought the graph could never touch the asymptote.

Answer 4

@IrishBoy123

Answer 5

correct, the graph will never touch the asymptote. in my simplified example, using the core function ie 1/exp(x*x), that will just get smaller and smaller and smaller as x tends to plus or minus infinity. it will never get there because infinity is not a number but a concept akin to eternity.

in the more complex example that you cited, yes the asymptote has been shifted up the y-axis but the analysis is the same.

the picture i posted came from an excel spreadhseet and maybe the graph thickness gives the idea that the graph eventually settles out at zero. it doesn't, that just sloppiness from me. it never ever reaches the asymptote. you never get to infinity.

Answer 6

you need a better handle. from what i can see you have a very fine mind. keep on keeping on!