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Question 7 • Algebra II

Which of the following is the graph of f of x is equal to absolute value of x translated 2 units right, 2 units up, and dilated by a factor of 1 third ?

Answer

Image with description On a coordinate plane, the scale on the x and y axes ranges from negative 3 to 7 in increments of 1. The graph represents the shifted absolute value function. The V-shaped graph is facing up. The vertex is at (2 comma 2), and the function passes through (1 comma 5) and (3 comma 5).

Image with description On a coordinate plane, the scale on the x and y axes ranges from negative 3 to 7 in increments of 1. The graph represents the shifted absolute value function. The V-shaped graph is facing up. The vertex is at (negative 2 comma 2), and the function passes through (negative 5 comma 3) and (1 comma 3).

Image with description On a coordinate plane, the x and y axes range from negative 3 to 7 in increments of 1. The V-shaped graph opening upward has a vertex at (2 comma 2) and the graph passes through the points (negative 1 comma 3) and (5 comma 3).

Image with description On a coordinate plane, the x and y axes are listed from negative 3 to 7 in increments of 1. The V-shaped graph opening upward has a vertex at (2 comma negative 2) and the graph passes through the points (0 comma 4) and (4 comma 4).

Explanation

Translating |x| 2 units right and 2 units up gives a vertex at (2, 2). Dilating vertically by a factor of 1/3 gives f(x) = (1/3)|x − 2| + 2. Moving 3 units left or right from the vertex raises the graph by (1/3)(3) = 1, so it passes through (−1, 3) and (5, 3), as shown in choice C.

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