Which of the following correctly identifies the transformations undergone from f(x)=|x| to f(−x)+6=|−x|+6?(1 point)

Question

Responses

reflected across the y-axis and translated down vertically
reflected across the y -axis and translated down vertically

reflected across the x-axis and translated down vertically
reflected across the x -axis and translated down vertically

reflected across the x-axis and translated up vertically
reflected across the x -axis and translated up vertically

reflected across the y-axis and translated up vertically

Answer 1

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

1. The expression \( | -x | \) reflects the graph of \( |x| \) across the y-axis. This is because substituting \( -x \) for \( x \) reverses the x-coordinates of every point on the graph. Therefore, this transformation is a reflection across the y-axis.

2. The \( +6 \) in \( f(-x) + 6 \) indicates a vertical translation upwards by 6 units.

Putting it all together, the transformations from \( f(x) = |x| \) to \( f(-x) + 6 \) involve:

• Reflecting across the y-axis
• Translating vertically upwards by 6 units

Thus, the correct identification is:

reflected across the y-axis and translated up vertically.

If that option were available, it would be the correct choice. However, since the option correctly identifying these transformations as upward translations is absent, please confirm the options provided or check for any discrepancies.