The Cube Root Function — Quiz

Question 4 • Algebraic Reasoning

The graph of y is equal to cube root of x is reflected over the y -axis and then translated down 2 units to form f of x Which is the graph of f of x ?

Answer

Image with description On a coordinate plane, the x-axis ranges from negative 10 to 10 in increments of 2, and the y-axis ranges from negative 5 to 5 in increments of 1. A curve goes through the point negative 3 comma negative 1, the point negative 2 comma 0, and the point negative 1 comma 1.

Image with description On a coordinate plane, the x-axis ranges from negative 10 to 10 in increments of 2, and the y-axis ranges from negative 5 to 5 in increments of 1. A curve goes through the point negative 1 comma negative 1, the point 0 comma negative 2, and the point 1 comma negative 3.

Image with description On a coordinate plane, the x-axis ranges from negative 10 to 10 in increments of 2, and the y-axis ranges from negative 5 to 5 in increments of 1. A curve goes through the point 1 comma 1, the point 2 comma 0, and the point 3 comma negative 1.

Image with description On a coordinate plane, the x-axis ranges from negative 10 to 10 in increments of 2, and the y-axis ranges from negative 5 to 5 in increments of 1. A curve goes through the point negative 1 comma 1, the point 0 comma 2, and the point 1 comma 3.

Explanation

Reflecting y = ∛x over the y-axis replaces x with −x, giving y = ∛(−x) = −∛x. Translating the graph down 2 units gives f(x) = −∛x − 2. For example, this graph passes through (−1, −1), (0, −2), and (1, −3), which matches choice B.

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