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

Question

to f(−x)−3=|−x|−3
?(1 point)
Responses

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

reflected across the y-axis and translated horizontally to the left
reflected across the y -axis and translated horizontally to the left

reflected across the y-axis
reflected across the y -axis

reflected across the x-axis and translated up

Answer 1

To analyze the transformation from \( f(x) = |x| \) to \( f(-x) - 3 = | - x | - 3 \), we can break it down into steps:

1. Reflection across the y-axis: The transformation \( f(-x) \) reflects the graph of \( f(x) = |x| \) across the y-axis. Since \( |-x| = |x| \), this step does not change the appearance of the graph (the graph remains the same).

2. Translation downward: The term "-3" in \( f(-x) - 3 \) translates the graph downward by 3 units.

Putting it all together, we see that:

• The reflection across the y-axis does not alter the shape of the absolute value function because \( | - x | \) is equivalent to \( |x| \).
• The graph is moved down 3 units.

Thus, the correct identification of the transformations undergone is:

Reflected across the y-axis and translated down.