What is the relationship between the independent and dependent variables in a function?

In a function, the relationship between the independent and dependent variables is that the independent variable determines the values of the dependent variable. The independent variable is the one that you can control or manipulate, while the dependent variable is the one that responds to changes in the independent variable.

For example, if you have a function that describes the relationship between the temperature of a substance (independent variable) and its state (solid, liquid, gas) (dependent variable), changing the temperature will directly affect the state of the substance. Thus, the value of the dependent variable depends on the value you choose for the independent variable.

This relationship is fundamental to understanding functions in mathematics; it emphasizes the cause-and-effect dynamic where the changes in the independent variable lead to changes in the dependent variable, making option A the correct choice.