Question

Which of the following describes how to translate the graph y = |x| to obtain the graph of y = |x + 1| + 1?

Answer 1

Translation: Move left 1 and up 1

Explanation:

The form is always y = |x - h| + k, where h is horizontal movement and k is vertical movement. So,

From the parent graph, you are moving up 1, as k has been added as a positive one. h would be -1, and would be moving to the left because it is negative (and going with the number line). To check, plug the values in (h as -1 and k as 1):

y = |x| (Parent)

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

y = |x + 1| + 1 (Final answer)