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Question 8 • Algebra 1

Which graph represents the function f of x is equal to negative start absolute value x plus 3 end absolute value ?

Answer

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

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

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

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

Explanation

The expression inside the absolute value, x + 3, is zero when x = −3, so the graph’s vertex is (−3, 0). The negative sign in front reflects the usual absolute-value graph downward. For example, f(−4) = −|−1| = −1 and f(0) = −|3| = −3, matching the graph with vertex (−3, 0) that opens downward: choice B.

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