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 left 2

Answer 1

To create the function \( g(x) \) as a translation of the function \( f(x) = |x| \), we need to consider how the graph is transformed.

You mentioned that the graph of \( g(x) \) was "went left 2." This means we are translating the function \( f(x) \) 2 units to the left.

The general form for translating the function \( f(x) = |x| \) left by \( h \) units is given by:

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

In this case, since we are translating it left by 2 units, \( h = 2 \):

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

In the given form \( a|x - h| + k \), we can rewrite it:

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

Here, \( a = 1 \), \( h = -2 \), and \( k = 0 \).

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

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

or in the requested form:

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

To summarize:

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

So, the answer is \( g(x) = 1|x + 2| + 0 \) or simply \( g(x) = |x + 2| \).