The Cube Root Function — Quiz

Question 7 • Algebra 2 with Probability

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

Answer

Image with description A coordinate plane with a curve. The x-axis is labeled from negative 10 to 10 in increments of 2 and the y-axis is labeled from negative 5 to 5 in increments of 1. A curve begins with an arrow near the point negative 10 comma 3 at the upper left, decreases gradually through the second quadrant, passes through approximately the point 0 comma 1 on the y-axis, and continues decreasing through the fourth quadrant, ending with an arrow near the point 8 comma negative 3 at the lower right, forming an S-shaped curve with a negative overall direction.

Image with description A coordinate plane with a curve. The x-axis is labeled from negative 10 to 10 in increments of 2 and the y-axis is labeled from negative 5 to 5 in increments of 1. A curve begins with an arrow near the point negative 10 comma negative 3 at the lower left, increases gradually through the third quadrant, passes through the origin, and continues increasing through the first quadrant, ending with an arrow near the point 4 comma 3 at the upper right, forming an S-shaped curve with a positive overall direction.

Image with description A coordinate plane with a curve. The x-axis is labeled from negative 10 to 10 in increments of 2 and the y-axis is labeled from negative 5 to 5 in increments of 1. A curve begins with an arrow near the point negative 10 comma 2 at the left, decreases gradually through the second quadrant, passes through the origin, and continues decreasing through the fourth quadrant, ending with an arrow near the point 10 comma negative 3 at the lower right, forming an S-shaped curve with a negative overall direction.

Image with description A coordinate plane with a curve. The x-axis is labeled from negative 10 to 10 in increments of 2 and the y-axis is labeled from negative 5 to 5 in increments of 1. A curve begins with an arrow near the point negative 10 comma negative 2 at the lower left, increases gradually through the third quadrant, passes through the origin, and continues increasing through the first quadrant, ending with an arrow near the point 8 comma 2 at the upper right, forming an S-shaped curve with a gentle positive slope.

Explanation

The graph of f(x) = ∛x increases from left to right and passes through the origin, since ∛0 = 0. It also passes through (−8, −2) and (8, 2), because ∛(−8) = −2 and ∛8 = 2. Choice B shows this increasing S-shaped curve through the origin, with endpoints near those values.

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