Question

Which of the following describes how to translate the graph y = |x| to obtain the graph of y = |x - 1| - 1? 1 unit left and 1 unit down 1 unit left and 1 unit up 1 unit right and 1 unit down 1 unit right and 1 unit up

Answer 1

1 unit right and one unit down

Explanation:

Answer 2

1 unit right and 1 unit down

Explanation:

When you replace x with x - h, you translate the graph h units horizontally.

When you replace y with y - k, you translate the graph k units vertically.

y = |x - 1| - 1

y + 1 = |x - 1|

y - (-1) = |x - 1|

Compare the last equation above with y = |x|. x was replaced by x - 1, so h = 1, and the translation is 1 unit horizontally. Since 1 is positive, it is a 1 unit translation to the right. y was replaced by y - (-1), so k = -1, and the vertical translation is 1 unit down.