Absolute Value Functions — Quiz

Question 19 • Algebraic Reasoning

Which of the following is the graph of f of x is equal to negative 0 point 5 start absolute value x plus 3 end absolute value minus 2 ?

Answer

Image with description On a coordinate plane, the scale on the x and y axes ranges from negative 7 to 3 in increments of 1. The graph represents the shifted absolute value function. The V-shaped graph is facing down. The vertex is at (negative 3 comma negative 2), and the function passes through (negative 5 comma negative 3) and (negative1 comma negative 3).

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 down. The vertex is at (3 comma 2), and the function passes through (negative 1 comma 0) and (7 comma 0).

Image with description On a coordinate plane, the scale on the x and y axes ranges from negative 7 to 3 in increments of 1. The graph represents the shifted absolute value function. The V-shaped graph is facing up. The vertex is at (negative 3 comma negative 2), and the function passes through (negative 7 comma 0) and (1 comma 0).

Image with description On a coordinate plane, the scale on the x and y axes ranges from negative 2 to 8 in increments of 1. The graph represents the shifted absolute value function. The V-shaped graph is facing up. The vertex is at (3 comma 2), and the function passes through (negative 1 comma 6) and (7 comma 6).

Explanation

The function is f(x) = −0.5|x + 3| − 2. Since x + 3 = x − (−3), its vertex is (−3, −2), and the negative coefficient means the V opens downward. At x = −5 or x = −1, the distance from −3 is 2, so f(x) = −0.5(2) − 2 = −3. Choice C has this vertex and passes through those points.

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