Overview
On this page we review the standard “Cartesian” coordinate plane (named after René Descartes, 1596-1650), and the concepts of relations and functions and how to represent them.
Basic Learning Objectives
These are the tasks you should be able to perform with reasonable fluency when you arrive at your next class meeting. Important new vocabulary words are indicated in italics.
- Understand the Cartesian coordinate plane, identify the \(x\)-axis, \(y\)-axis, and quadrants, and be able to plot a given point \((a,b)\) in this plane.
- Understand the concept of a relation and be able to represent it as either a table, mapping, or a graph.
- Understand the meaning of domain and range of a relation, and identify these for a given relation.
Advanced Learning Objectives
In addition to mastering the basic objectives, here are the tasks you should be able to perform after class, with practice:
- Understand the special property a relation needs to satisfy to be a function.
- Verify whether a given graph represents a function using the vertical line test.
To prepare for class
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Watch the following video (by mathantics, 10m13s) which reviews the Cartesian coordinate plane, the \(x\)- and \(y\)-axes, quadrants, and how to plot points in this plane:
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Watch the the first part of the following video (by iteachalgebra, up to 9m04s) which explains the meaning of a relation, shows how to represent it either as a table, mapping, or graph, and how to identify the domain and range of the relation:
After class
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Watch the following video (by mathantics, 11m23s) which introduces the concept of a function, explains how to use the vertical line test to recognize a function, and introduces the function notation \(f(x)\):
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Watch the following video (by Mathispower4u, 6m18s) which shows some more examples of how to determine whether a given relation is in fact a function:
