The graph shows g(x), which is a transformation of f(x)=|x|. Write the function rule for g(x).-10-8-6-4-2246810-10-8-6-4-22468100xy

To find the function rule for $g(x)$ based on the transformation of $f(x) = |x|$, we first need to analyze how the graph of $g(x)$ has been modified from $f(x)$.

Step 1: Identify Transformations

1. Vertical Shifts: Determine if the graph is moved up or down.
2. Horizontal Shifts: Determine if the graph is moved left or right.
3. Reflections: Check if the graph has been reflected over the x-axis or y-axis.
4. Stretches/Compressions: Analyze if the graph has been stretched or compressed vertically or horizontally.

Step 2: Write the Function Rule

Based on the transformations identified, we can express $g(x)$ as a function of $f(x)$.

1. Shift Down: If the graph of $g(x)$ is shifted down by a certain amount, subtract that amount from $f(x)$.
2. Horizontal Shift: If the graph shifts right by $h$, replace $x$ with $x - h$, or shift left by $h$ with $x + h$.
3. Reflections: If the graph is reflected across the x-axis, multiply $f(x)$ by -1.

Step 3: Analyze the Specific Graph

Without the actual graph to reference, the general rule can only be discussed. Assuming specific transformations could look something like this:

• If $g(x) = |x - 2| - 3$, this means the graph of $f(x)$ was shifted right by 2 and down by 3.

Step 4: Finalize the Function Rule

Once you confirm the transformations by analyzing the visual representation of the graph:

Final Answer

Write $g(x)$ in the appropriate form based on the transformations you've noted. For example, $g(x) = |x - h| + k$, where $h$ and $k$ are the horizontal and vertical shifts respectively.