Reflections and Dilations of Absolute Value Functions — Quiz

Question 3 • Mathematics II

Which graph represents the function f of x is equal to negative absolute value of x minus 2 ?

Answer

Image with description A V-shaped graph that opens upward, has vertex at 0 comma negative 2, and passes through the points negative 2 comma 0, and 2 comma 0.

Image with description A V-shaped graph that opens downward, has vertex at 0 comma 2, and passes through the points negative 2 comma 0, and 2 comma 0.

Image with description A V-shaped graph that opens downward, has vertex at 0 comma negative 2, and passes through the points negative 2 comma negative 4, and 2 comma negative 4.

Image with description A V-shaped graph that opens upward, has vertex at 0 comma 2, and passes through the points negative 2 comma 4, and 2 comma 4.

Explanation

For f(x) = -|x| - 2, the negative sign makes the absolute-value graph open downward. Subtracting 2 shifts its vertex from (0, 0) to (0, -2). At x = -2 or x = 2, f(x) = -2 - 2 = -4, so the graph with vertex (0, -2) and points (-2, -4) and (2, -4) is choice C.

AI-written and checked against the verified answer.

More from this Course

Quiz

Quiz

Quiz