Which of the following correctly identifies the transformations undergone from f(x)=|x| to f(-x)+6= |-x|+6

To analyze the transformation from \( f(x) = |x| \) to \( f(-x) + 6 = |-x| + 6 \), let's break it down step by step:

1. Identifying the function \( f(-x) \):

   • \( f(x) = |x| \)
   • \( f(-x) = |-x| \)
   • The transformation from \( f(x) \) to \( f(-x) \) reflects the function across the y-axis. This is because replacing \( x \) with \( -x \) defines a reflection across the y-axis.

2. Identifying the vertical translation:

   • The full expression \( f(-x) + 6 = |-x| + 6 \) indicates that we are taking the graph of \( |-x| \) and translating it vertically upwards by 6 units.

So, the transformations that occur from \( f(x) = |x| \) to \( f(-x) + 6 = |-x| + 6 \) are:

• Reflected across the y-axis (from \( |x| \) to \( |-x| \))
• Translated up vertically by 6 units (from \( |-x| \) to \( |-x| + 6 \))

Therefore, the correct answer is:

Reflected across the y-axis and translated up vertically.