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© 2014 Pacific Crest
261
6.2
Symbolic, Graphical, Numerical Representations
P
urpose
The role this topic plays in quantitative reasoning
Relationships between quantities can be represented in a variety of ways. Each method of representation
yields different information and can aid you in your efforts to understand those relationships. The purpose
of this experience is to give you the opportunity to explore the kinds of information and understanding that
can be gleaned from the three major categories of representation: Symbolic, Graphical, and Numerical.
When reasoning quantitatively and solving problems, what we think of as creativity often comes when
we manage to see things from different perspectives. Gaining facility working with the three types of
representation covered here will strengthen your ability to shift perspectives and thus be more creative
in your quantitative reasoning and problem solving.
L
earning Goals
What you should learn while completing this activity
1. Understand the benefits and potential issues of using each type of representation.
2. Transform a symbolic representation of a relationship to a numerical one
3. Transform between numerical and graphical representations of a relationship
4. Decide which representation will be the most valuable for current context.
5. Describe the dynamics of a relationship by using different representations.
D
iscovery
Finding out for yourself
Using this contents of this book, identify two examples each of symbolic, graphical, and numerical
representations of relationships. Describe the characteristics of each type of representation in terms of
the following:
●
the relationship represented
●
the specific quantities in that relationship
●
maximum and minimum values for each quantity
●
any type of rate (increase/decrease) represented
●
interesting features of the relationship
W
hat Do You Already Know?
Tapping into your existing knowledge
1. How do you know what the numbers in a table represent?
2. How do you graph the points in a two column numerical table on a coordinate plane?
3. What are the
domain
and
range
of a function?
4. What are four symbolic representations of different types of functions? (For example,
f
(
x
) = 2
x
+ 3
is an example of a linear function.)