Reflections and Dilations of Absolute Value Functions — Quiz

Question 6 • Mathematics II

Which graph represents the function f of x is equal to 1 third absolute value of x ?

Answer

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

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

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

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

Explanation

The function f(x) = (1/3)|x| has its vertex at the origin and rises by 1 for every 3 units moved horizontally. For example, when x = 3 or x = -3, f(x) = (1/3)(3) = 1, so the graph passes through (-3, 1) and (3, 1). That matches choice B.

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