Reflections and Dilations of Absolute Value Functions — Quiz

Question 8 • Mathematics II

Which graph represents the function f of x is equal to negative start absolute value x minus 2 end absolute value minus 1 ?

Answer

Image with description A V-shaped graph that opens downward, has vertex at negative 2 comma negative 1, and passes through the points negative 4 comma negative 3, and 0 comma negative 3.

Image with description A V-shaped graph that opens upward, has vertex at negative 2 comma negative 1, and passes through the points negative 3 comma 0, and negative 1 comma 0.

Image with description A V-shaped graph that opens upward, has vertex at 2 comma negative 1, and passes through the points 1 comma 0, and 3 comma 0.

Image with description A V-shaped graph that opens downward, has vertex at 2 comma negative 1, and passes through the points 0 comma negative 3, and 4 comma negative 3.

Explanation

The function is f(x) = −|x − 2| − 1. The expression x − 2 shifts the absolute-value graph 2 units right, so its vertex is (2, −1). The negative sign in front makes the graph open downward; for example, at x = 0 and x = 4, f(x) = −3. Choice D has this vertex, direction, and pair of points.

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