Question

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

Explanation:

Step1: Recall translation of absolute value function

The parent function is \( f(x) = |x| \), which has its vertex at \((0,0)\). The general form of a translated absolute value function is \( g(x) = |x - h| + k \), where \((h,k)\) is the vertex of the new function.

Step2: Identify the vertex of \( g(x) \)

From the graph, the vertex of \( g(x) \) is at \((2,0)\). So, \( h = 2 \) and \( k = 0 \).

Step3: Substitute \( h \) and \( k \) into the general form

Substituting \( h = 2 \) and \( k = 0 \) into \( g(x) = |x - h| + k \), we get \( g(x) = |x - 2| + 0 \), which simplifies to \( g(x) = |x - 2| \).

Answer:

\( g(x) = |x - 2| \)