Study Guides (390,000)
CA (150,000)
Ryerson (10,000)
BUS (50)
BUS 100 (10)

BUS 100 Study Guide - Linear Equation, Graphing Calculator, Cartesian Coordinate System


Department
Business
Course Code
BUS 100
Professor
Marla Spergel

This preview shows pages 1-3. to view the full 62 pages of the document.
Math Skills for Business- Full Chapters
86
U4 Full Chapter 11- Graphing in the Coordinate Plane
11.1 Introduction to Graphing
A graph may be regarded as a pictorial representation of data. A graph may be drawn
manually on paper, or by using software on a graphing calculator or computer.
Graphs, especially of functions are mostly drawn on a rectangular co-ordinate plane.
A rectangular co-ordinate plane is formed by the intersection of two number lines.
One, on the East-West directions is called the horizontal axis, and the other on the
North-South directions is called the vertical axis. The horizontal and vertical axis,
make up the co-ordinate axis, and divide the co-ordinate plane into four regions
called quadrants (fig. 1).
Why a Co-ordinate Plane? Because a point on a co-ordinate plane is also identified as
the ordered pair of numbers (horizontal co-ordinate, vertical co-ordinate), and an
ordered pair of numbers interpreted as (horizontal co-ordinate, vertical co-ordinate) is
identified as a point on a co-ordinate plane. The horizontal co-ordinate is the number
on the horizontal axis, and the vertical co-ordinate is the number on the vertical axis
associated with the point on the co-ordinate plane.
0
First Quadrant
Second Quadrant
QQQuadrant
Third Quadrant
QQQuadrant
Fourth Quadrant
vertical axis
fig. 1

Only pages 1-3 are available for preview. Some parts have been intentionally blurred.

Math Skills for Business- Full Chapters
87
In (fig. 2) the points A, B, C, D are also indentified by the attached pair of
numbers. The ordered pairs (2, 3), (-5, 4), (-3.5, -6), (3,-2.5) are the points attached.
NOTE: In fig.2, the letter x is representing the horizontal axis and in such a case the
horizontal axis becomes the x-axis, and similarly the vertical axis is the y-axis. It
should be noted that the axis can be assigned any names.
Graph of Functions:
What is a function? For our purpose, it is a set of instructions and procedures which
takes a number called the INPUT NUMBER to produce another number called the
0
x
o
r
i
z
o
n
t
a
l
y
1
2
3
4
5
1
2
3
4
-1
-2
-4
-3
-5
5
-6
-6
-2
-1
-3
-4
-5
*(2,3)
*(-5,4)
*(-3.5,-6)
*(3,-2.5)
*A(3,2)
*B(0,5)
*C(4,-5)
*A(-6,0)
fig. 2

Only pages 1-3 are available for preview. Some parts have been intentionally blurred.

Math Skills for Business- Full Chapters
88
OUTPUT NUMBER. The set of instructions and procedures are given either by
words (e.g. XX), or by algebraic equations (e.g. YY). Therefore the function is also
given by the set of ordered pair of numbers (INPUT NUMBER, Corresponding
OUTPUT NUMBER) of the function for all possible input numbers.
Function is:
And also the set of ordered pair of numbers (INPUT NUMBER, OUTPUT
NUMBER) for each input number and its corresponding output number.
The ordered pair of numbers (INPUT NUMBER, OUTPUT NUMBER) is also a
point on a co-ordinate plane whose horizontal axis is the INPUT NUMBERS and the
vertical axis is the OUTPUT NUMBERS. For such a coordinate plane the horizontal
axis is called the INPUT-axis, and the vertical axis the OUTPUT-axis.
The graph of a function is always on such a coordinate plane, and it is all the points
with coordinates (INPUT NUMBER, corresponding OUTPUT NUMBER).
How is the graph of a function constructed?
1. Choose a letter (e.g. t) or word (e.g. distance) to represent the INPUT numbers,
and a different letter (e.g. q) or (e.g. amount) to represent the OUTPUT
numbers if they are not given. From the examples, the horizontal axis is then
the t-axis and the vertical axis the q-axis.
2. Make a table (of values) with the headings INPUT (eg t), OUTPUT (eg q), and
(INPUT, OUTPUT) {eg (t, q)}. From the possible INPUT numbers choose
about 11 different numbers if the function if not linear and 4 numbers if
it is a linear function. For each INPUT number chosen find the corresponding
OUTPUT number and the ordered pair of numbers (INPUT, OUTPUT).
3. With the INPUT and OUTPUT numbers from (2) as a guide choose a scale for
the INPUT (horizontal) and OUTPUT (vertical) axis and draw both axis.
INPUT NUMBER
Instructions
and
Procedure machine
OUTPUT NUMBER
You're Reading a Preview

Unlock to view full version