Question

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

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

Answer 1

"Reflected across the y-axis and translated up vertically."

Reason: f(-x) is a reflection across the y-axis, and +6 shifts the graph up 6 units. (For |x| the reflection is not visible because |x| is even, but the operation is a y-axis reflection.)