Answer:
\(f(x)=\frac{1}{3}|(x+2)|\)
Step-by-step explanation:
We have been given a function \(f(x)=|\frac{1}{3}x|\). We are asked to translate the function to 2 units to the left.
We know that an absolute function is form \(y=a|x-h|+k\), where, (h,k) is vertex.
Let us recall translation rules.
\(f(x)\rightarrow f(x-a)=\text{Graph shifted to right by a units}\)
\(f(x)\rightarrow f(x+a)=\text{Graph shifted to left by a units}\)
\(f(x)\rightarrow f(x)+a=\text{Graph shifted upwards by a units}\)
\(f(x)\rightarrow f(x)-a=\text{Graph shifted downwards by a units}\)
Absolute value of 1/3 will be 1/3.
\(f(x)=\frac{1}{3}|x|\)
Therefore, our required function would be \(f(x)=\frac{1}{3}|x+2|\).
