In a mathematical function, what does one quantity depend on?

In a mathematical function, one quantity is defined as dependent on another quantity when the value of the dependent quantity is determined by the value of the independent quantity. This relationship indicates that changes in the independent variable will produce consistent and predictable changes in the dependent variable.

For example, in the function ( y = 2x + 3 ), the value of ( y ) consistently depends on the value of ( x ). If we change ( x ), we can calculate a corresponding value for ( y ) based on the established rule of the function. This dependency is fundamental to the concept of functions, where the dependent variable is often represented on the vertical axis of a graph, while the independent variable is on the horizontal axis. This understanding is crucial in various fields of mathematics and its applications in science, economics, and engineering.

The other choices do not accurately describe the relationship in a function. Independence implies no correlation between quantities, randomness suggests unpredictability without any defined relationship, and exponential growth describes a specific type of change in a variable rather than the dependency relationship itself.