Answer:
The functions \( f(x) = 4|x-1| \) and \( f(x) = |4x-1| \) do not have the same graph.
1. The function \( f(x) = 4|x-1| \) is a transformation of the absolute value function \( f(x) = |x| \) where the graph is vertically stretched by a factor of 4 and shifted 1 unit to the right.
2. On the other hand, the function \( f(x) = |4x-1| \) is a transformation of the absolute value function \( f(x) = |x| \) where the graph is horizontally compressed by a factor of 1/4 and shifted 1/4 unit to the right.
These transformations result in different graphs for the two functions. Therefore, \( f(x) = 4|x-1| \) and \( f(x) = |4x-1| \) do not have the same graph.
Step-by-step explanation:
