Question

The graph shows g(x), which is a translation of f(x)=|x|. Write the function rule for g(x). Write your answer in the form a|x–h|+k, where a, h, and k are integers or simplified fractions. went up 2
g(x)=

Answer 1

To write the function rule for \( g(x) \) as a translation of \( f(x) = |x| \), we need to know the transformations applied to \( f(x) \).

You mentioned that the graph of \( g(x) \) went "up 2". This indicates a vertical translation. The general form of the transformation for a vertical shift is:

\[
g(x) = f(x) + k
\]

where \( k \) is the vertical shift. In this case, since the graph goes up by 2, we have \( k = 2 \).

Next, since you want the expression in the form \( a|x - h| + k \), we need to configure it accordingly. Since \( |x| \) itself has no horizontal shift (meaning \( h = 0 \)), and there’s also no vertical compression/stretch (implying that \( a = 1 \)), we can set:

- \( a = 1 \)
- \( h = 0 \)
- \( k = 2 \)

Thus, we substitute these values into the transformation:

\[
g(x) = 1|x - 0| + 2
\]

This simplifies to:

\[
g(x) = |x| + 2
\]

So the function rule for \( g(x) \) is:

\[
g(x) = |x| + 2
\]