Which of the following correctly identifies the transformations undergone from f(x)=|x|

Question

to f(−x)+6=|−x|+6
?(1 point)

Answer 1

To go from \( f(x) = |x| \) to \( f(-x) + 6 = | -x | + 6 \), we can identify the following transformations:

1. Reflection across the y-axis: The function changes from \( f(x) = |x| \) to \( f(-x) = |-x| \). Since \( |-x| = |x| \), this step does not change the shape of the function, but it reflects it.

2. Vertical shift upward: The addition of 6 in \( f(-x) + 6 \) translates the entire function upward by 6 units.

Therefore, the transformations from \( f(x) = |x| \) to \( f(-x) + 6 = | -x | + 6 \) include a reflection across the y-axis followed by a vertical shift up by 6 units.