Graph of x³ (the cubic y = x³)

Updated 20 October 2026 · Values computed by the ihateDesmos engine

The graph of y = x³ is an S-shaped curve that rises everywhere, from −∞ on the left to +∞ on the right. It flattens out for a moment at the origin, where it changes from bending down to bending up.

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The graph of

y=x³

for −3 ≤ x ≤ 3. Dots mark its root.

Key features

Domain: All real numbers
Range: All real numbers
Root: x = 0 (a triple root)
Inflection point: (0, 0), where the tangent is horizontal
Monotonic: Increasing everywhere
Symmetry: Odd: (−x)³ = −x³, symmetric about the origin
y-intercept: None
Derivative: 3x²
Antiderivative: 14x⁴+C

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

What the graph of x³ looks like

Unlike x², cubing keeps the sign: negative inputs give negative outputs. So the graph comes up from −∞ in the third quadrant, passes through the origin, and goes on to +∞ in the first.

At the origin the slope 3x² is zero, but the function keeps increasing: this is a stationary point of inflection, not a maximum or minimum. The curve is concave down for x < 0 and concave up for x > 0.

Near the origin the graph is very flat (0.5³ = 0.125), and away from it very steep (3³ = 27). General cubics ax³ + bx² + cx + d keep the S-shape but can have a hump and a dip.

Points of interest

Found numerically to about twelve digits in the window −3 ≤ x ≤ 3, 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: (0, 0)

Table of values

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

Values of x³
x	y = x³
−3	−27
−2	−8
−1	−1
0	0
1	1
2	8
3	27

How to graph x³ by hand

1
Plot (0, 0), (1, 1), (−1, −1), (2, 8) and (−2, −8).
2
Add (0.5, 0.125) and (−0.5, −0.125) to capture the flat stretch near the origin.
3
Draw a smooth S-curve that is horizontal at the origin and steepens outward.

Transformations

How the graph moves when you change the formula. The original is x³ in blue.

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y = (x - 1)^3 + 2 The inflection point moves to (1, 2).
y = -x^3 Reflected: now decreasing everywhere.
y = x^3 - 3x Adding −3x creates a local maximum at (−1, 2) and a minimum at (1, −2).