vertically compressed by a factor of 1/3

Answer 1

Say if you have an absolute value function f(x)= |4-x|, the way you would vertically compress it is by affecting it's slope. If you multiply the number in front of x by 1 1/3 or 1.3333 repeating. The 1 aspect of 1 and 1/3 helps the slope stay constant, the 1/3 or .3333 repeating compresses it vertically by 1/3. Without adding the 1 in front and just multiplying by 1/3 or .333 repeating would actually do the opposite which is expand the function. You are looking to increase the slope, not decrease the slope and that is what vertical compression does.

Your new function equation is: f(x)= |4-1.3333x|

Some would think to multiply the entire expression by 1.3333 but that would affect the y-intercept at: f(x)= |5.3333-1.3333x= 5.3333-1.333(0). So focusing on the number in front of x compresses without shifting it up by 1.3333.

Graphing the function will help you to better visualize the change in the function.