Determine whether each equation defines y as a function of x. x = (1/3)(y^2)

Key Concepts

Function Definition

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output. In mathematical terms, for a relation to be a function, no two ordered pairs can have the same first element with different second elements. This concept is crucial for determining if an equation defines one variable as a function of another.

Vertical Line Test

The vertical line test is a visual way to determine if a curve is a function. If any vertical line intersects the graph of the relation at more than one point, then the relation does not define y as a function of x. This test helps in understanding the graphical representation of functions and their properties.

Solving for y

To determine if an equation defines y as a function of x, it is often necessary to solve the equation for y. This involves isolating y on one side of the equation. If the resulting expression for y can be expressed as a single output for each input x, then y is a function of x; otherwise, it is not.