Determine whether each function graphed or defined is one-to-one. y = -1 / x+2

Key Concepts

One-to-One Function

A one-to-one function is a type of function where each output value is associated with exactly one input value. This means that no two different inputs produce the same output. To determine if a function is one-to-one, one can use the horizontal line test: if any horizontal line intersects the graph of the function more than once, the function is not one-to-one.

Graphing Rational Functions

Rational functions are expressed as the ratio of two polynomials. The function given, y = -1/(x + 2), is a rational function that can be graphed to analyze its behavior. Understanding the asymptotes, intercepts, and overall shape of the graph is crucial for determining properties like whether it is one-to-one.

Horizontal Line Test

The horizontal line test is a visual method used to determine if a function is one-to-one. If any horizontal line drawn across the graph intersects the curve at more than one point, the function fails the test and is not one-to-one. This test is particularly useful for analyzing the graphs of functions quickly and effectively.