N/A — Exam

Question 11 • Algebra II

Which graph represents y is equal to cube root of x plus 6 minus 3 ?

Answer

Image with description Coordinate plane with x- and y-axes labeled. The x-axis and y-axis are labeled from negative 8 to 8 in increments of 2. An increasing S-shaped curve is shown. The curve passes through approximately (negative 8 comma 4), (2 comma 5), (3 comma 6), and (8 comma 8). The central bend of the curve is located near (3 comma 6).

Image with description On a coordinate plane x and y axes range from negative 9 to 9 in increments of 1. A graph of cubic function passes through points (negative 8 comma negative 4), (0 comma negative 1), and (8 comma negative 0 point 5). The curve has a point of inflection at (negative 6 comma negative 3).

Image with description Coordinate plane with x- and y-axes labeled. The x-axis and y-axis are labeled from negative 8 to 8 in increments of 2. An increasing S-shaped curve is shown. The curve passes through approximately (negative 8 comma 4), (negative 3 comma 6), (negative 1 comma 7), and (8 comma 8). The central bend of the curve is located near (negative 3 comma 6).

Image with description On a coordinate plane x and y axes range from negative 9 to 9 in increments of 1. A graph of cubic fucntion passes through points (negative 5 comma negative 5), (0 comma negative 5), and (5 comma negative 4). The curve has a point of inflection at (6 comma negative 3) and passes through (9 comma negative 1 point 5).

Explanation

The graph of y = ∛(x + 6) − 3 is the basic cube-root curve shifted 6 units left and 3 units down. Its central point, where the curve bends, is therefore (−6, −3). Choice B has that central point and also matches nearby values, such as y ≈ −1 when x = 0.

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