Question

A function is defined by \(z=x^{2} y-x y^{2} .\) Identify the independent and dependent variables.

Short answer

Answer: In the given function, \(x\) and \(y\) are independent variables, while \(z\) is the dependent variable.

Step-by-step solution

Identify the Variables

The function given is \(z = x^2y - xy^2\). The variables involved are \(x\), \(y\), and \(z\). Now we need to determine their roles in the function.

Identify the Inputs and Output

In a function, the independent variables are typically considered the inputs, while the dependent variable is considered the output. In this case, we find that: 1. \(x\) and \(y\) can both be changed (or manipulated) without affecting the other. Thus, they are both independent variables. 2. The value of \(z\) is based on the values of \(x\) and \(y\). It depends on them, making it the dependent variable.

State the Independent and Dependent Variables

After analyzing the function \(z = x^2y - xy^2\), we have found that the independent variables are \(x\) and \(y\), while the dependent variable is \(z\).