Graphing Radical Functions — Quiz

Question 5 • Algebra 2 with Probability

Which graph represents y is equal to cube root of x ?

Answer

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 2 comma negative 8), (negative 1 comma negative 1), the origin, (1 comma 1), and (2 comma 8). The point of inflection is at the origin.

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 2), (0 comma 0), and (8 comma 2). The curve has a point of inflection at the origin.

Image with description On a coordinate plane x and y axes range from negative 9 to 9 in increments of 1. The graph has a parabola opening upwards and has a vertex at (0 comma 0). It passes through (negative 2 comma 4) and (2 comma 4)

Image with description On a coordinate plane x and y axes range from negative 9 to 9 in increments of 1. The curve originates from the origin and passes through points (1 comma 1), (4 comma 2), and (8 comma 3) in the 1st quadrant.

Explanation

For y = ∛x, the output is the cube root of each x-value: ∛(−8) = −2, ∛0 = 0, and ∛8 = 2. So the graph passes through (−8, −2), (0, 0), and (8, 2), which matches choice C. Choice A shows y = x³, the inverse relationship.

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