# 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.

#### Explanation:

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#