The problem asks to describe the transformations necessary to convert the graph of $f(x) = |x|$ into that of $g(x) = -|x| + 2$.

Step-by-step breakdown:

1. Reflection: The function $f(x) = |x|$ produces a V-shaped graph that opens upwards. In $g(x) = -|x| + 2$, the negative sign in front of the absolute value reflects the graph across the x-axis. This changes the graph from opening upwards to opening downwards.

2. Translation: The "+2" outside the absolute value indicates a vertical translation. The entire graph is shifted up by 2 units.

Conclusion:

The transformation involves reflecting the graph across the x-axis and then translating it up 2 units.

Thus, the correct answer is:

• Reflect across the x-axis, translate up 2 units.

Would you like further explanation or have any questions?

Here are 5 related questions to deepen your understanding:

1. What kind of transformations affect the shape of a graph but not its position?
2. How do horizontal translations affect the equation of a graph?
3. How would the graph of $g(x) = |x| - 2$ compare to that of $f(x) = |x|$?
4. What would happen if the graph were reflected across the y-axis instead of the x-axis?
5. How would adding a coefficient in front of $x$ inside the absolute value (e.g., $f(x) = |2x|$) affect the graph?

Tip: Always pay close attention to signs when dealing with reflections.