Question
Which of the following correctly identifies the transformations undergone from f(x)=|x|
to f(−x)+6=|−x|+6
?(1 point)
to f(−x)+6=|−x|+6
?(1 point)
Answers
GPT-4o mini
To go from \( f(x) = |x| \) to \( f(-x) + 6 = | -x | + 6 \), we can identify the following transformations:
1. **Reflection across the y-axis**: The function changes from \( f(x) = |x| \) to \( f(-x) = |-x| \). Since \( |-x| = |x| \), this step does not change the shape of the function, but it reflects it.
2. **Vertical shift upward**: The addition of 6 in \( f(-x) + 6 \) translates the entire function upward by 6 units.
Therefore, the transformations from \( f(x) = |x| \) to \( f(-x) + 6 = | -x | + 6 \) include a reflection across the y-axis followed by a vertical shift up by 6 units.
1. **Reflection across the y-axis**: The function changes from \( f(x) = |x| \) to \( f(-x) = |-x| \). Since \( |-x| = |x| \), this step does not change the shape of the function, but it reflects it.
2. **Vertical shift upward**: The addition of 6 in \( f(-x) + 6 \) translates the entire function upward by 6 units.
Therefore, the transformations from \( f(x) = |x| \) to \( f(-x) + 6 = | -x | + 6 \) include a reflection across the y-axis followed by a vertical shift up by 6 units.