Graph of the cube root: y = ∛x

Updated 20 October 2026 · Values computed by the ihateDesmos engine

Unlike the square root, the cube root works for negative numbers too: ∛(−8) = −2. Its graph is an S-shape lying on its side, passing through the origin with a vertical tangent and rising everywhere.

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The graph of

y=∛x

for −10 ≤ x ≤ 10. Dots mark its root.

Key features

Domain: All real numbers
Range: All real numbers
Root: x = 0
Inflection point: (0, 0), with a vertical tangent
Perfect-cube points: (±1, ±1), (±8, ±2), (±27, ±3)
Symmetry: Odd: ∛(−x) = −∛x
y-intercept: None
Derivative: 13x²³
Antiderivative: 3x⁴³4+C

Derivative and antiderivative from the calculator’s algebra system. Domain, range and asymptotes are stated for real x.

What the graph of ∛x looks like

The cube root is the inverse of x³, so its graph is the cubic reflected in the line y = x. The cubic’s flat point at the origin becomes a vertical tangent here.

Because a negative number has a real cube root, the graph continues into the third quadrant, symmetric to the first. Some calculators draw only the right half of x^(1/3), treating it as a complex power; this calculator returns the real cube root.

It grows even more slowly than √x for large x: you need x = 1000 to reach 10.

Points of interest

Found numerically to about twelve digits in the window −10 ≤ x ≤ 10, then shown in exact form where one exists.

x-intercepts (roots): x = 0
Local maxima: None in this window
Local minima: None in this window
Inflection points: None in this window

Table of values

A few points to plot, with exact values where they are simple.

Values of ∛x
x	y = ∛x
−27	−3
−8	−2
−1	−1
0	0
1	1
8	2
27	3

How to graph ∛x by hand

1
Plot (0, 0), (1, 1), (8, 2) and their mirror images (−1, −1) and (−8, −2).
2
Draw the curve vertically through the origin and bend it to flatten outward on both sides.

Transformations

How the graph moves when you change the formula. The original is ∛x in blue.

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y = cbrt(x - 4) Shifted right 4: the vertical tangent moves to x = 4.
y = 2cbrt(x) Vertically stretched by 2.
y = -cbrt(x) + 1 Reflected and shifted up 1: decreasing, crossing the x-axis at x = 1.

Frequently asked questions

What is the domain of the cube root function?

All real numbers. Every real number, including negatives, has exactly one real cube root.

Why does my calculator not graph x^(1/3) for negative x?

Some calculators evaluate fractional powers of negative numbers as complex numbers and drop them. Mathematically, the real cube root of −8 is −2, which is what this calculator returns for both cbrt(x) and x^(1/3).

Is the cube root function differentiable at 0?

No. Its tangent at the origin is vertical, so the derivative 1/(3x^(2/3)) is infinite there.