In Exercises 11–26, determine whether each equation defines y as a function of x. x + y = 16

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 y as a function of x.

Vertical Line Test

The vertical line test is a visual way to determine if a curve is a graph of a function. If any vertical line intersects the graph at more than one point, the relation is not a function. This test helps to quickly assess whether y can be expressed uniquely for each x in a given equation.

Solving for y

To determine if an equation defines y as a function of x, it is often useful to solve the equation for y. If the equation can be rearranged to express y solely in terms of x, it indicates that y is a function of x. For example, in the equation x + y = 16, isolating y gives y = 16 - x, confirming that y is indeed a function of x.