Question

Which graph represents the function f(x) = −|x − 2| − 1?

Answer 1

f(x) = −|x − 2| − 1 is an inverted V (absolute-value) graph with

- vertex at (2, −1) (maximum),
- opens downward (because of the leading −),
- left branch (x < 2): y = x − 3,
- right branch (x ≥ 2): y = −x + 1,
- y-intercept at (0, −3),
- no x-intercepts,
- domain (−∞, ∞), range (−∞, −1].

So pick the graph that is a downward-pointing V with its peak at (2, −1), symmetric about x = 2, passing through (0, −3).