In Exercises 11–26, determine whether each equation defines y as a function of x. |x|- y = 5

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 in analyzing equations graphically to see if they meet the criteria of a function.

Absolute Value Function

The absolute value function, denoted as |x|, outputs the non-negative value of x regardless of its sign. This function creates a V-shaped graph, which can lead to multiple outputs for a single input when solving equations. Understanding how absolute value affects the relationship between x and y is essential for determining if the given equation defines y as a function of x.