Stretches and Compression of Trig Functions

Today's and yesterday's we learned about the stretching and compressing of trig functions.

Vertical stretches and compressions:

• if y = af(x) the entire graph stretches vertically by a factor of "a" units
• if y = 1/a f(x) the entire graph compresses vertically by a factor of "a" units

Note: only the y value changes.

Horizontal stretches and compression:

• if y = f(ax) the entire graph compresses horizontally by a factor of "a" units.
• if y = f(1x/a) the entire graph stretches horizontally by a factor of "a" units.

Note: only the x value changes.

Example # 1

Red:

As you can see the basic function became more compressed because of 2

Blue:

This is the basic function.

Green:

As you can see the function was stretched because of 1/2

Example # 2

This is the basic cos function.

As you can see the graph shifted to the left by 90 degrees and down 1

here is a link that can help explain the transformation of functions: http://www.regentsprep.org/Regents/math/algtrig/ATP9/funclesson1.htm