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 4
g(x)=

Answer 1

To write the function rule for \( g(x) \), which is a translation of \( f(x) = |x| \), we need to determine how \( g(x) \) is transformed from \( f(x) \).

Since you mentioned that the graph of \( g(x) \) "went up 4," we know that this is a vertical translation. To translate \( f(x) \) upward by 4 units, we add 4 to the function:

\[
g(x) = f(x) + 4 = |x| + 4
\]

In the requested format \( g(x) = a|x - h| + k \):

- \( a = 1 \) (since there is no vertical stretching or compression)
- \( h = 0 \) (no horizontal translation, as there is no shift left or right)
- \( k = 4 \) (the vertical shift)

Thus, the function rule for \( g(x) \) is:

\[
g(x) = 1|x - 0| + 4
\]

In simplified form, you can write:

\[
g(x) = |x| + 4
\]

Therefore, the final answer is:

\[
g(x) = |x| + 4
\]