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 function

The parent function is \( f(x) = |x| \), which has its vertex at \( (0,0) \). For \( g(x) \), the vertex is at \( (5,0) \), so it's a horizontal translation. The general form for horizontal translation of \( |x| \) is \( |x - h| \), where \( h \) is the horizontal shift.

Step2: Determine the shift

Since the vertex moves from \( (0,0) \) to \( (5,0) \), \( h = 5 \). So the function rule for \( g(x) \) should be \( g(x)=|x - 5| \).

Answer:

\( g(x) = |x - 5| \)