Square Root and Cube Root Functions — Test

Question 20 • Algebra 2 with Probability

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

Answer

Image with description On a coordinate plane, the x and y axes ranging from negative 9 to 9 in increments of 1, with major tick marks at even integers. A parabolic curve, opening upwards, has its vertex at the origin (0 comma 0). The curve passes through points such as (1 comma 1), (negative 1 comma 1), (2 comma 4), and (negative 2 comma 4).

Image with description On a coordinate plane, the x and y axes ranging from negative 9 to 9 in increments of 1, with major tick marks at even integers. A curve starts at the origin (0 comma 0). The curve extends upwards and to the right, passing through points (1 comma 1), (4 comma 2) and (8 comma 3) in first quadrant.

Image with description On a coordinate plane, the x and y axes ranging from negative 9 to 9 in increments of 1, with major tick marks at even integers. A curve passes through the origin (0 comma 0). The curve increases from the bottom left to the top right, passing through points such as (negative 2 comma negative 8), (negative 1 comma negative 1), (1 comma 1), and (2 comma 8).

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.

Explanation

For y = ∛x, the x-values −8, 0, and 8 give y-values −2, 0, and 2, respectively, because (−2)³ = −8 and 2³ = 8. The graph also has the characteristic increasing, S-shaped curve with an inflection at the origin. Choice C matches these points and shape; choice A instead shows y = x³.

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