When we replace f(x) with f(1/3(x-2)), it means that we are making a transformation to the original function f(x) = |x|.
To understand the effects on the graph, let's break down the transformation step by step:
1. First, let's consider the expression inside the absolute value function: 1/3(x-2). This expression represents a horizontal compression and translation of the original function.
2. The 1/3 coefficient in front of (x-2) causes a horizontal compression. This means that the graph will be narrower compared to the original graph of f(x) = |x|. The compression factor is determined by the reciprocal of the coefficient, so the graph will be compressed horizontally by a factor of 3.
3. The (x-2) term inside the parentheses represents a horizontal translation. Specifically, it shifts the graph 2 units to the right compared to the original graph of f(x) = |x|.
4. Combining the effects of the compression and translation, we can conclude that the graph of f(1/3(x-2)) will be narrower and shifted 2 units to the right compared to the original graph of f(x) = |x|.
To summarize, the effects on the graph of f(x) = |x|, when f(x) is replaced by f(1/3(x-2)), are a horizontal compression by a factor of 3 and a horizontal translation of 2 units to the right.