The graph in the image shows two functions:

• $f(x) = |x|$ in red, which is the absolute value function, forming a "V" shape.
• $g(x)$ in blue, which looks like a vertical shift or transformation of $f(x)$.

To identify $g(x)$, observe how the blue graph differs from the red graph of $f(x)$.

Observations:

• The graph of $g(x)$ seems to be vertically translated downward compared to $f(x)$.
• Specifically, $g(x)$ appears to be shifted by 2 units downward.

Conclusion:

The transformation can be written as: $g(x) = |x| - 2$ This is because shifting $f(x) = |x|$ downward by 2 units modifies the graph accordingly.

Would you like more details or have any further questions? Here are five related questions for further practice:

1. What would happen if we shifted $f(x) = |x|$ by 3 units upward instead of downward?
2. How do you reflect $f(x) = |x|$ across the x-axis to form a new function?
3. What is the result of shifting $f(x) = |x|$ 2 units to the right?
4. How would you describe the effect of multiplying $f(x) = |x|$ by a constant greater than 1?
5. What happens when you apply a horizontal stretch to $f(x) = |x|$?

Tip: Always check for vertical or horizontal shifts when identifying transformations in functions.