C3 functions

http://www.examsolutions.net/a-level-maths-papers/Edexcel/Core-Maths/Core-Maths-C3/2009-June/paper.php#Q5

part c i don't understand why the range is just -k

usually i let x=0 and e to the 0 makes 1 so from my logic(which isn't right this time) i got 1-k

e^(2x) is always greater than zero (draw the graph)

So e^(2x)-k is always greater than -k.

For the graph f(x) = e^x, you know there is an asymptote at f(x) = 0.

If the graph is e^2x, the asymptote will not move.

The -k means all y values go downwards by k, and hence, since y must be greater than 0, it now must be greater than -k.