Objective [1.4]-Problems - Solutions
Choose symbols and write out functional notation for a “functional” relationship (i.e. function)
For each functional relationship statement identify the input and output and define appropriate symbols(letters) for each. Then
define a symbol(letter) for the functional relationship and write out the relationship in functional notation. Also “retranslate” back
into English using the symbols and then all in English using the word “function”
Note: In general x, y, and f are not appropriate choices. Also, symbols choices will vary from person to person but as long they are
defined it is fine.
Example: “There is a relationship between time and average price of a home”
Solution:
Define:
Functional Notation:
English:
Input: Let “time” be t.
Output: Let “average home price be” be p.
Relationship: Let the functional relationship be H
p=H(t)
“p is a function, H, of t” or just “p is a function of t”
“average home price is a function of time”
Solutions Submitted by Zhi cao Pan
1. There is a relationship between course grade and student satisfaction
Input: Let“course grade”be c
Define:
Output: Let “student satisfaction”be s
Relationship: Let the functional relationship be I
Functional Notation: s=I(c)
“s is a function, I, of c”or just “s is a function of c”
English:
“student satisfaction is a function of course grade.”
2. Time invested determines course grade.
Input: Let “time invested”be t
Define:
Output: Let “course grade”be c
Relationship: Let the functional relationship be L
Functional Notation: c=L(t)
“c is a function, L ,of t”“c is a function of t”
English:
“course grade is a function of time invested”
3. Price of a product is related to demand for that product
Input: Let “demand for that product”be d
Define:
Output: Let “price of a product”be p
Relationship: Let the functional relationship be H
Functional Notation: p=H(d)
“p is a function, H, of d” “p is a function of d”
English:
“price of a product is a function of demand for that
product.”
4. Average unit cost of a product is determined by the units produced
Input: Let “the units produced”be u
Output: Let “average unit cost of a product”be
Define:
a
Relationship: Let the function relationship be S
Functional Notation: a=S(u)
“a is a function ,S ,of u” “a is a function of u”
English:
“Average unit cost of a product is a function of the
units produced.”
5. Shipping time affects customer satisfaction
Input: Let “Shipping time”be s
Define:
Output: Let “customer satisfaction”be c
Relationship: Let the function relationship be O
Functional Notation: c=O(s)
“c is a function ,O ,of s” “c is a function of s”
English:
“customer satisfaction is a function of shipping time.”
6. Repeat business is influenced by perceived value
Input: Let “perceived value”be p
Define:
Output: Let “repeat business”be r
Relationship: Let the functional relationship be K
Functional Notation: r=K(p)
“r is a function ,K ,of p” “r is a function of p”
English:
“Repeat business is a function of perceived value”
7. Sales are related to advertising expenditures
Input: Let “advertising expenditures”be a
Define:
Output: Let “sales”be s
Relationship: Let the functional relationship be U
Functional Notation: s=U(a)
“s is a function ,U ,of a” “s is a function of a”
English:
“sales is a function of advertising expenditures”
8. The purchasing manager’s index (PMI) changes in time
Input: Let “time”be t
Let “the purchasing manager’s
Define:
index” be p
Relationship: Let the functional relationship be M
Functional Notation: p=M(t)
“p is a function ,M ,of t” “p is a function of t”
English:
“The purchasing manager’s index is a function of
time”
9. The purchasing manager’s index (PMI) has an effect on unemployment
Input: Let “PMI”be p
Define:
Output: Let “unemployment”be u
Relationship: Let the functional relationship be J
Functional Notation: u=J(p)
“u is a function ,J ,of p” “u is a function of p”
English:
“unemployment is a function of PMI”