Principle behind compressing trig functions

Hi!

What's the idea behind compressing functions when graphing, compressing horizontally or vertically:

1. $\displaystyle y = \sec 2x\ \text{versus}\ 2 \sec x$

There is no amplitude, what's the function of the second **2**?

2. $\displaystyle y = \sec \frac12x\ \text{versus}\ \frac12 \sec x$

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Re: Principle behind compressing trig functions

Consider the function $\displaystyle y_1 = f(x)$ -- if the constant A is introduced then the function $\displaystyle y_1=Af(x)$ will be stretched vertically by factor A, and the function $\displaystyle y_3=f(Ax)$ will be squeezed horizontally by factor A. Here is an example where $\displaystyle y_1 = sin(x)$ and A = 3. See how $\displaystyle y_2 = 3sin(x)$ is streteched vertically while its period remains the same, and $\displaystyle y_3 = sin(3x)$ is squeezed horizontally while it's height remains the same?