easy graph-I am having a mental block (1 Viewer)

[shazzam]

y= x-e^[-x], find the x intercepts. Also if I use limits it seems to me that y approaches infinity quite fast, however it is no so in the answers....please help, this stress is makin' my brain work even less

 

[acmilan]

As x approaches infinity, y is approximately equal to x so y = x is an assymptote

 

[shazzam]

this graph has two branches. Yes, that's right that y--> x is an asymptote, however that only applies to the section of the graph below that line (y=x). For the other branch, x--> -infinity y should become infintely small as e^-x becomes very large, however that would mean it eventually cutting y=x...yes this is gay

 

[tempco]

When x -> - infinity, doesnt the function approach - infinity too? For y = x - e^(-x), y = e^(-x) is a lot larger than y = x for any value of x which is negative. So subtracting e^(-x) from x will result in a value approaching - infinity...

 

[shazzam]

indeed nekkid, thus one would think that the left hand branch of this graph would cut y=x at some point right? since it decreases faster...?

 

[Heinz]

It doesnt cut it at all actually. y = x - e^(-x) stays below the line y=x for all x.

 

[tempco]

Yeh since it's x - e^(-x), when considering positive values of x, e^(-x) approaches 0 from positive y-values, so the graph will always be lower than y = x