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263
S
trategies
T
ransforming
FROM N
umerical
R
epresentation
From/To
N
umerical
→
S
ymbolic
See
7.4 Correlation and Regression
Process
Computer software is used to generate curves that fit the data.
Benefits
Possible Issues
1. Concise notation
2. Can parameterize
3. Generalization
4. Set patterns of behaviors
5. Use in modeling
The type of curve that should be fit to the data in a
table may be difficult to determine.
Reason
Some information about a relationship can be easily determined from its
symbolic representation.
From/To
N
umerical
→
G
raphical
See
2.5 Analyzing a Function
6.3 Graphical Analysis
Process
Each row of the table can represent a point on the graph. Graph enough points to
have a reasonable idea of the graphical representation of the relationship.
Benefits
Possible Issues
1. Visualize relationships
2. Identify trends
3. Study boundary conditions
4. Find quickly maximums and minimums
5. Graphical analysis
Using the finite numerical points can miss features of
an accurate graphical representation of the relationship.
The points can only be approximately placed on the
coordinate axes.
Reason
Graphical information can give different information from numerical/tabular
display of a relationship.
O
ops
! A
voiding
C
ommon
E
rrors
●
Using too large an increment when transforming from symbolic to numerical form
Example
: Creating a table of the
function
f
(
x
) =
x
3
– 3
x
using increments of 2
units:
x
f
(
x
)
–6 –198
–4 –52
–2 –2
0
0
2
2
4 52
6 198
Why?
The table is missing information
that is critical to understanding the
relationship the function describes.
The points chosen makes the graph
look like a logistic function with
one root (at 0) rather than the three
roots of a third-order polynomial
(with roots at 0 and
3
±
).
●
Not using a consistent delta distance in a table of values when analyzing a relationship
Example
: The growth of the children in a family measured at different times periods in their life
(e.g., Sally’s height is measured at ages 2, 4, and 7; Jimmy’s is measured at ages 3, 4,
and 11)
6.2 Symbolic, Graphical, Numerical Representations