The Cube Root Function — Quiz

Question 9 • Algebraic Reasoning

The function f of x is equal to cube root of x is reflected over the x -axis to create the graph of g of x is equal to negative cube root of x Which is the graph of g of x ?

Answer

Image with description On a coordinate plane, a cube root function goes through negative 8 comma 2, has an inflection point at 0 comma 0, and goes through 8 comma negative 2.

Image with description On a coordinate plane, a cube root function goes through negative 8 comma negative 2, has an inflection point at 0 comma 0, and goes through 8 comma 2.

Image with description On a coordinate plane, a cube root function goes through negative 2 comma negative 8, has an inflection point at 0 comma 0, and goes through 2 comma 8.

Image with description On a coordinate plane, a cube root function goes through negative 2 comma 8, has an inflection point at 0 comma 0, and goes through 2 comma negative 8.

Explanation

Reflecting a graph over the x-axis changes each point (x, y) to (x, −y). Since the cube root of −8 is −2 and the cube root of 8 is 2, the graph of g(x) = −∛x passes through (−8, 2), (0, 0), and (8, −2). Choice A shows these points.

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