41) The graph shows \( g(x) \), which is a translation of \( f(x)=|x| \). Write the function rule for \( g(x) \).

To determine the function rule for \( g(x) \) based on the translation of \( f(x) = |x| \), we need to identify the specific translations involved. If the graph of \( g(x) \) appears shifted horizontally and/or vertically from \( f(x) \), that will give us the information we need to formulate \( g(x) \). For instance, if \( g(x) \) is shifted right by 3 units and down by 2, the function rule would be \( g(x) = |x - 3| - 2 \). If the graph shifted left or up instead, for instance, the rule would adjust accordingly. Identify the specific shifts to write the correct rule! To ensure you handle shifts correctly, always plot the original function \( f(x) = |x| \) and compare it with \( g(x) \). Remember that horizontal shifts are influenced by the x-term in the absolute value, while vertical shifts modify the entire function. Common mistakes occur when people swap these shifts or forget to account for their direction!