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

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: $g \left(x\right) = a f \left(x\right)$

Assuming (in this case) $f \left(x\right) = x \mathmr{and} p \left(x\right) = f \left(x\right)$
and $a = \frac{1}{3}$

In even simpler simpler terms, every y point is equal to $\frac{1}{3} x$
So if $x = 1$ then $y = \frac{1}{3}$