Question

Which absolute value function, when graphed, represents the parent function, f(x) = |x|, reflected over the x-axis and translated 1 unit to the right?

f(x) = –|x| + 1
f(x) = –|x – 1|
f(x) = |–x| + 1
f(x) = |–x – 1|

Answer 1

f(x) = −|x − 1|

Reason: Reflecting |x| over the x-axis gives −|x|. Translating right 1 replaces x by (x − 1), giving −|x − 1|.