A simple Math 12 question:

Consider a) y=x and b) y=5x.

So, b) is vertically expanded by a factor of 5 compared to a) right?

Can I also say that it is horizontally compressed by a factor of 5, and vertically compressed by a factor of 1/5?

Thanks.

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- September 16th 2008, 05:24 PMbonehelmIs Vertical expansion the same as horizontal compression?
A simple Math 12 question:

Consider a) y=x and b) y=5x.

So, b) is vertically expanded by a factor of 5 compared to a) right?

Can I also say that it is horizontally compressed by a factor of 5, and vertically compressed by a factor of 1/5?

Thanks. - September 17th 2008, 11:08 AMTKHunny
Yes and No.

For simpler forms, it is easy enough to see that you CAN design a vertical expansion that looks like any given horizontal compression. This does not mean they are the same thing, only that the result is the same.

Odd Example

$1 = 50¢+50¢

$1 = 25¢+25¢+25¢+25¢

$1 = 25¢+25¢+25¢+10¢+10¢+5¢

It's still a dollar, you just get there different ways.

More-to-the-point example

Start at (0,0).

Walk Up 1 - You are at (0,1)

Walk Right 1 - You are at (1,1)

Remember that and do this.

Start at (0,0).

Walk Right 1 - You are at (1,0)

Walk Up 1 - You are at (1,1)

You ended up in the same place, but took a different path to get there.

It may not seem all that important, and often it isn't. As long as things are nice and continuous and well-behaved it is likely no one cares. When you start adding singularities, it requires greater care. Ask Han Solo! "*Traveling through hyperspace ain't like dusting crops, boy. Without precise calculations we could fly right through a star or bounce too close to a supernova, and that'd end your trip real quick, wouldn't it?*"