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Identifying Independent and Dependent Variables

publish date: 2026/05/23 18:30:34.604040 UTC

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In the equation \(y = f(x) = e^x\), how are the roles of \(x\) and \(y\) classified?

\(x\) is the dependent variable; \(y\) is the independent variable

\(x\) is the independent variable; \(y\) is the dependent variable

Both \(x\) and \(y\) are independent variables

Both \(x\) and \(y\) are dependent variables

Correct Answer

\(x\) is the independent variable; \(y\) is the dependent variable

Explanation

In \(y = f(x)\), \(x\) is the independent variable — we choose it freely. \(y\) (or \(f(x)\)) is the dependent variable — its value is completely determined by whichever \(x\) we choose. The formula \(f\) is the rule linking the two.

Reference

Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012

Quizzes you can take where this question appears

Foundations of Function Notation and Representation