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 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

Answer 1

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

1. Reflection across the y-axis: The function \( f(-x) \) indicates that we are replacing \( x \) with \( -x \). The absolute value function \( |x| \) is symmetric about the y-axis, so \( | -x | \) is equal to \( | x | \). Thus, this step does not introduce any new transformations.

2. Translation vertically: The addition of 6, as in \( f(-x) + 6 = | -x | + 6 \), translates the graph upward by 6 units.

Now, we consider the transformations:

• The function is reflected across the y-axis (due to the \( -x \) input).
• It is translated up vertically by 6 units due to the addition of 6.

Thus, the correct identification is:

Reflected across the y-axis and translated up vertically.