Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Re: e^x
Replies: 0

 Mark Howell Posts: 28 Registered: 12/6/04
Re: e^x
Posted: Feb 24, 1998 2:14 PM

>Again, this is a unique property of the exponential function. A vertical shift
>is the same as a vertical stretch. So the A and C are different arbitrary
>constants, but if chosen correctly, they will result in the same particular
>solution.
>

Er, you mean a horizontal shift is the same as a vertical stretch?
i.e. e^(x-h) = ke^x, true when k = e^-h.

In Doug's case, Ae^x = e^x+C only when A=1 and C=0 i.e. for e^x.

On a loosely related note, I've use the corresponding property

ln(x) + ln(a) = ln(ax)
i.e. a vertical *shift* is the same as a horizontal *stretch*.

The analagous property holds for the exponential, of course,
since "vertical" is translated to "horizontal" when talking