Basic HTML Version
Q
uantitative
R
easoning &
P
roblem
S
olving
262
© 2014 Pacific Crest
M
athematical Language
Terms and notation
graphical representation
— a relationship is projected by plotting a set of table values from a
symbolic representation
numerical representation
— a table of values organized to show the relationship between two or
more variables
symbolic representation
— a relationship expressed as an equation, function, or formula
I
nformation
What you need to know
Quantitative reasoning requires that we are able to constantly shift the representation of relationships in
order to increase our understanding of a problem that we are analyzing or solving. Nearly every experience
in this book involves the changing of a representation in order to improve or clarify understanding. While
the specific cases of transformation are legion, there are really only four transformations represented in
this book:
to numerical
representation (fromsymbolic and graphical) and
fromnumerical
representation
(to symbolic and graphical).
S
trategies
T
ransforming
TO N
umerical
R
epresentation
From/To
S
ymbolic
→
N
umerical
See
2.5 Analyzing a Function
Process
Make a table with the first column representing values of the variable and the
second column determined from the symbolic representation
Benefits
Possible Issues
1. Use in future computations
2. Easier to graph
3. Find specific values
The table can miss features of the symbolic version
since only a finite number of points can be displayed in
a table.
Reason
Tables are used to create the graphical representation of the relationship
From/To
G
raphical
→
N
umerical
See
6.3 Graphical Analysis and
6.1 Interpreting Graphs and Diagrams
Process
For each row of the numerical table, draw lines through a point on the graph
perpendicular to the horizontal and vertical axes. The point of intersection of
these lines with the horizontal axis will give the first column number, the vertical
intersection will give the second column number.
Benefits
Possible Issues
1. Locating specific values
2. Use in future computations
3. Create new relationships
4. Analyze using data and statistical techniques
The numbers in a table generated in this way are only
approximate.
Reason
Actual numerical values are sometimes important in determining the maximum
and minimum values of the relationship.