N/A — Exam

Question 29 • Algebraic Reasoning

Which graph represents the function g of x is equal to start absolute value x plus 4 end absolute value plus 2 ?

Answer

Image with description A coordinate plane has both the axis labeled from negative 6 to 6. An absolute value graph has a vertex at negative 2 comma 4.

Image with description A coordinate plane has both the axis labeled from negative 6 to 6. An absolute value graph has an upward facing V shaped curve with vertex at 4 comma 2.

Image with description A coordinate plane has both the axis labeled from negative 6 to 6. An absolute value graph has an upward facing V shaped curve with a vertex at 2 comma 4.

Image with description A coordinate plane has both the axis labeled from negative 6 to 6. An absolute value graph has a vertex at negative 4 comma 2.

Explanation

The function is g(x) = |x + 4| + 2. In the form |x − h| + k, the vertex is (h, k). Since x + 4 = x − (−4), the vertex is (−4, 2), and the graph opens upward. Choice D has a vertex at (−4, 2).

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