Cubic and Cube Root Functions and Equations — Test

Question 11 • Algebra II

Which is the graph of the cube root function f of x is equal to cube root of x ?

Answer

Image with description On a coordinate plane, a cube root function goes through negative 4 comma negative 2, has an inflection point at 0 comma 0, and goes through 4 comma 2.

Image with description On a coordinate plane, a cube root function goes through negative 4 comma 2, has an inflection point at 0 comma 0, and goes through 4 comma negative 2.

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 thorugh 8 comma 2.

Explanation

For f(x) = ∛x, the cube root of −8 is −2, and the cube root of 8 is 2. The graph also passes through (0, 0), so choice A, which includes (−8, −2), (0, 0), and (8, 2), is correct. Choices C and D have the signs reversed, and B uses x-values that do not match these cube roots.

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