Answer:
The correct option is 4.
Step-by-step explanation:
The given function is,
[tex]f(x)=\frac{1}{3}|x|[/tex]
It is a modulus function and its parent function is,
[tex]g(x)=|x|[/tex]
In a function,
[tex]f(x)=k|x|[/tex]
If k>1, then the graph of g(x) stretch vertically and if k<1 then the graph of g(x) compressed vertically.
Since k is [tex]\frac{1}{3}[/tex], therefore the shoes the vertical compression.
put x=0 in the given function.
[tex]f(0)=\frac{1}{3}|0|=0[/tex]
Put x=3.
[tex]f(3)=\frac{1}{3}|3|=1[/tex]
Therefore the graph passing through (0,0) and (3,1).
Thus fourth option is correct.
