What is the graph of y = -x^3?

The graph of \( y = -x^3 \) is a cubic curve that is reflected in the x-axis.

In more detail, the equation \( y = -x^3 \) represents a cubic function where the coefficient of \( x^3 \) is negative. This negative coefficient causes the graph to be reflected in the x-axis compared to the graph of \( y = x^3 \). The basic shape of a cubic graph is an S-curve, but in this case, it will start from the top left, pass through the origin, and then move to the bottom right.

At \( x = 0 \), the value of \( y \) is also 0, so the graph passes through the origin (0,0). As \( x \) becomes more positive, \( y \) becomes more negative, and as \( x \) becomes more negative, \( y \) becomes more positive. This creates a curve that slopes downwards from left to right.

The graph is symmetric with respect to the origin, meaning if you rotate it 180 degrees around the origin, it looks the same. This symmetry is a characteristic of odd functions, which \( y = -x^3 \) is an example of. The steepness of the curve increases as you move away from the origin, reflecting the cubic nature of the function.

Understanding the graph of \( y = -x^3 \) helps in visualising how changes in the equation affect the shape and direction of the curve, which is a key skill in GCSE Maths.