4 ## INTRODUCTION TO GRAPHSThe coördinate pairs of a function WE WILL BEGIN with some basic vocabulary. First, a coördinate. A coördinate is a number. It labels a point on a line. The coördinates 0, 1, 2, 3, etc. label those points. They are the "addresses" of those points. A coördinate axis is a line with coördinates. To label the points in a plane, we will need more than one coördinate axis, and we place them at right angles. Hence, they are called rectangular coördinate axes. And the coördinates on them are called rectangular coördinates. They are also called Cartesian coördinates, after the 17th century philosopher and mathematician René Descartes, for he was one of the first to exploit the geometrical possibilities of coördinates. Finally, the rectangular coördinates of a point are an ordered pair, (
Example 1. The graph of a In which graph are the values of To see the answer, pass your mouse over the colored area. In graph a). To each value of The coördinate pairs of a function Consider the function ( -- because the In other words, the graph of a function
is that geometrical figure such that every coördinate pair on it is ( The For example, if
then every coördinate pair on its graph has the form ( Problem 1. The coördinate pairs on the graph of the following functions have what form? To see the answer, pass your mouse over the colored area.
Problem 2. Let
Problem 3. Which of these points are on the graph of the function y = 2
Problem 4. a) The coördinate pair ( What is the relationship between the coördinates
b) The coördinate pair (
What is the relationship between the coördinates
The height of the graph at Let
Now, if While if Please make a donation to keep TheMathPage online. Copyright © 2017 Lawrence Spector Questions or comments? E-mail: themathpage@nyc.rr.com |