In Exercises 11–26, determine whether each equation defines y as a function of x. y = - √x +4

Key Concepts

Function Definition

A function is a relation that assigns exactly one output (y) for each input (x). This means that for every value of x in the domain, there is a unique corresponding value of y. To determine if an equation defines y as a function of x, we must check if each x-value leads to one and only one y-value.

Vertical Line Test

The vertical line test is a visual way to determine if a graph represents 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 an equation defines y as a function of x by examining its graphical representation.

Square Root Function

The square root function, represented as y = -√x + 4, involves taking the square root of x, which can yield both positive and negative values. However, since the equation specifies y as a negative square root, it will produce a unique y-value for each non-negative x-value, thus satisfying the definition of a function.