What type of graph is represented by the equation y = -x³?

The equation ( y = -x^3 ) represents a cubic graph because it is structured as a polynomial of degree three. In polynomial functions, the degree is determined by the highest power of the variable ( x ). Here, ( x ) is raised to the third power, indicating it’s a cubic function.

Cubic graphs have specific characteristics, such as having one or two turning points and extending infinitely in both directions. The presence of the negative sign before the ( x^3 ) term also indicates that the graph will have a particular orientation, showing that as ( x ) increases, ( y ) will decrease, particularly beyond the turning point, resulting in a downward slope from the left to the right.

Linear graphs represent a first-degree polynomial, quadratic graphs correspond to second-degree polynomials, and exponential graphs involve constants raised to a variable power, which are all fundamentally different in their structure and behavior than cubic graphs. Thus, recognizing the degree of the polynomial helps in understanding that the equation provided is indeed a cubic function.