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Chapter 1: Problem 2

Is the independent variable of a function associated with the domain or range? Is the dependent variable associated with the domain or range?

Short Answer

Expert verified
In a function, the independent variable (x) is associated with the domain, which represents all possible input values for the function. On the other hand, the dependent variable (y) is associated with the range, which represents all possible output values produced by the function based on the independent variables within the domain.

Step by step solution

01

Understanding Independent and Dependent Variables

In a function, the independent variable is the one that can be manipulated, while the dependent variable is the one that is affected by the changes in the independent variable. In mathematical notation, we generally use "x" for the independent variable and "y" for the dependent variable. So, a function can be represented as y = f(x), where f(x) is a specific rule or relation, and x is the independent variable.
02

Definition of Domain and Range

The domain of a function is the set of all possible values of the independent variable (x-values) for which the function is defined. The range of the function is the set of all possible values of the dependent variable (y-values) that the function can produce as a result.
03

Independent Variable Association

The independent variable of a function is associated with the domain. The domain represents all the possible input values (x-values) that the independent variable can take.
04

Dependent Variable Association

The dependent variable of a function is associated with the range. The range represents all the possible output values (y-values) that the dependent variable can have as the independent variable changes within the given domain.

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