Question

Which of the following correctly identifies the transformations undergone from f(x)=|x| to f(−x)+6=|−x|+6 ?(1 point) Responses reflected across the y-axis and translated up vertically reflected across the y -axis and translated up vertically reflected across the x-axis and translated up vertically reflected across the x -axis and translated up vertically reflected across the x-axis and translated down vertically reflected across the x -axis and translated down vertically reflected across the y-axis and translated down vertically reflected across the y -axis and translated down vertically

Answer 1

To analyze the transformations from \( f(x) = |x| \) to \( f(-x) + 6 \):

1. Reflect across the y-axis: The transformation \( f(-x) \) indicates a reflection across the y-axis. This means that the graph of \( |x| \) is flipped over the y-axis, which results in the same graph since the absolute value function is even.

2. Translate up vertically: The addition of \( +6 \) signifies a vertical translation upward by 6 units.

Combining these two transformations, we find that from \( f(x) = |x| \) to \( f(-x) + 6 \), the correct answer is:

Reflected across the y-axis and translated up vertically.