Chapter 2.1, Problem 35AYU

In Problems 31-42, determine whether the equation defines $y$ as a function of $x$.

$y\text{ = }\sqrt[3]{x}$

To determine

To find: Whether the equation $y =\sqrt[3]{x}$ defines $y$ as a function of $x$.

Answer to Problem 35AYU

The equation is a function.

Explanation of Solution

Given:

The equation $y =\sqrt[3]{x}$

Calculation:

To determine whether the equation is a function, let us solve the equation for $y$

The curve $y =\sqrt[3]{x}$ passes through $\left(0,0\right)$. For any input of $x$, the equation yields only one output for $y$ , so the equation is a function.

For example for $x=1$ the equation yields $y=1$ and so on.