Which of the following describes the graph of 𝑦 = |𝑥| after it has been reflected across the x-axis, shifted vertically up 3 units, and shifted horizontally to the left 6 units?
The graph of 𝑦 = |𝑥| after being reflected across the x-axis, shifted vertically up 3 units, and shifted horizontally to the left 6 units will have the following characteristics:
1. Reflection across the x-axis: This will simply flip the graph of 𝑦 = |𝑥| upside down.
2. Vertical shift up 3 units: This will shift the entire graph of 𝑦 = |𝑥| vertically up by 3 units.
3. Horizontal shift to the left 6 units: This will shift the entire graph of 𝑦 = |𝑥| to the left by 6 units.
Therefore, the new graph will look like the original graph of 𝑦 = |𝑥| flipped upside down, shifted up 3 units, and shifted to the left 6 units.