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

Question

to f(−x)+6=|−x|+6
?(1 point)
Responses

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
reflected across the y -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 transformation from $f(x)=|x|$ to $f(-x)+6=|-x|+6$:

1. The expression $f(-x)$ represents a reflection across the y-axis because replacing $x$ with $-x$ in the function flips it horizontally.

2. The addition of $+6$ indicates a vertical translation upward by 6 units.

Therefore, the transformations undergone can be summarized as:

• Reflected across the y-axis
• Translated up vertically by 6 units

So, the correct response is:

reflected across the y-axis and translated up vertically.