Question

How do I graph the function p(x) = 1/3 | x | ?

Answer 1

Given the parent function

f(x) = |x|,

p(x) = 1/3 |x| = 1/3 f(x)

That is, p(x) is a vertical compression of f(x) by a factor of 1/3. This compression transforms the point (x, y) into (x, 1/3y).

x | f(x) | p(x)

-1 | |-1| = 1 | 1/3*1 = 1/3

0 | |0| =0 | 1/3*0 = 0

1 | |1| = 1 | 1/3*1 = 1/3

In the next graph, the plot of p(x) = 1/3 |x| is shown.