Question

Which graph represents the function r(x) = |x – 2| – 1

On a coordinate plane, an absolute value graph has a vertex at (2, negative 1).

On a coordinate plane, an absolute value graph has a vertex at (negative 2, negative 1).

Answer 1

The first graph (with vertex at (2, −1)).

Reason: r(x)=|x−2|−1 is of the form |x−h|+k with h=2 and k=−1, so the vertex is (2, −1). The V-shape opens upward with slopes ±1; e.g. r(0)=1 so the y-intercept is (0,1).