To translate f(x) right "h" units and up "k" units, make it be
f(x-h) + k
The ∨-shaped graph is the absolute value of x, |x|. To turn it upside down, make it be -|x| to reflect it across the x-axis.
(a) y = |x-1|-1 . . . . |x| translated 1 right and -1 up.
(b) y = 1-|x+1| . . . . -|x| translated -1 right and 1 up
