Graph of y = x³
Interactive graph of y = x³ (x cubed). Explore the cubic function, its inflection point, odd symmetry, and behavior with our free graphing calculator.
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Understanding the Function
The function y = x³ is the simplest cubic polynomial. Unlike the parabola, it passes through all four quadrants, rising steeply to the right and falling steeply to the left. The curve has an inflection point at the origin where it changes concavity.
Cubic functions are odd functions, meaning f(-x) = -f(x), which gives them rotational symmetry of 180 degrees about the origin. This property makes them useful in modeling phenomena that behave differently for positive and negative inputs, such as certain material stress-strain relationships.
The derivative of x³ is 3x², which is always non-negative, confirming that the function is always increasing (or flat at the origin). The second derivative is 6x, which changes sign at x = 0, confirming the inflection point there. The domain and range are both all real numbers.