Describing a Graph

Abstract

We take a moment here to informally provide common terminology used to describe a graph. This will allow us to learn some of language of a graph now. Eventually we will use calculus to identify parts of the graph with these characteristics. Figure 2.1 has these definitions which are informally given in M-Box 2.1. A graph is increasing when it is going up or rising. A graph is decreasing when it is going down or falling. A graph is concave up when it is curved upward. A graph is concave down when it is curved downward. An inflection point is where the concavity changes. A local max (or maximum) is a local high point of the graph. Graphs can have more than one local max. A local min (or minimum) is a local low point of the graph. Graphs can have more than one local min. A global max (or maximum) is the absolute highest point on the graph on a fixed interval. A global max may or may not be the same as a local max. A global min (or minimum) is the absolute lowest point on the graph on a fixed interval. A global min may or may not be the same as a local min.