How do you compare the graph of p(x) = 1/3x to the graph of f(x) = x?

1 Answer
Mar 3, 2017

Vertical Compression/Horizontal Stretch by a factor of 3.


Original Graph: (y = x)
graph{y = x}

Modified Graph: (y = 1/3x)
graph{y = 1/3x [-10, 10, -5, 5]}

From these two graphs you notice that there is a vertical compression (in the same manner, a horizontal stretch) according to transformations regarding the equation:

Because a vertical compression/horizontal stretch involves p(x) being modified by "a" factor between 0 and 1 (ie 1/3):

In universal terms: #g(x) = af(x)#

Assuming (in this case) #f(x) = x or p(x) = f(x)#
and # a = 1/3#

In even simpler simpler terms, every y point is equal to #1/3x#
So if #x = 1# then #y = 1/3#