HOIHU

1. Business Math
Prep. Year
Sheet 5
This sheet is going to cover the following topics:
Chapter 2: Functions, Special Functions and combinations of Functions:
• A function is a relationship (rule) that assigns to each input element or
number only one output element or number.
• Each function has a domain and a range.
• The domain is the subset of X consisting of all the x’s for which f(x) is
defined.
• The range is the set of all elements in Y of the form f(x)
 Polynomial function:
A function of the form: f(x) = cnxn
+cn-1 xn-1
+cn-2 xn-2
+…………. +c1 x+c0
Where n is nonnegative integer and cn, cn-1, …...., c0 are constants with cn≠0.
Some Types of polynomial Functions:
1. Constant Function:
A function of the form: h(x) =c
Where c is a constant.
2. Linear Function :
A function of the form: f(x) = c1 x+c0

2. 3. Quadratic Function:
A function of the form: f(x) = c2 x2
+c1 x+c0
 Rational Function:
A function that is a quotient of polynomial functions
(i.e. Every polynomial function is a Rational function)
 Case-defined Function:
A function where the rule specifying it, is given by several disjoint cases.
 Absolute-value Function:
|x|= x If x 0
-x If x 0
 Composite Function :
If f and g are functions, the composite of f with g is the function fоg
defined by
(fоg) (x) = f (g(x))
 Factorials:
It represents the product of the first r positive integers.
r!= 1.2.3……..r
We also define
0! =1

3. Class Discussion
Part one:
Give domain of each of the Functions:
1.
2.
1
1
)(


z
zf
Part two:
Part three:
Is y a function of x?
 9y-3x-4 =0
 Y=f(x); (x,y) = (-1,2), (0,3), (1,4), ( 2, 5)
 X=2y2
34)(  xxg
h
fhf
findxxfif
)3()3(
,35)(



4. Part four:
Word problems:
 Supply Function. Suppose the weekly supply function for a
kilogram of dates at Al Mokhtar Sweets store is p = q/48, where q
is the number of kilograms of dates supplied per week. How many
kg of dates per week will be supplied if the price is $8.39 a kg?
How many kg of dates per week will be supplied if the price is
$19.49 a kg? How does the amount supplied change as the price
increases?
 Hospital Discharges. An insurance company examined the records
of a group of individuals hospitalized for a particular illness. It
was found that the total proportion discharged at the end of t days
of hospitalization is given by
Evaluate (a) f(0), (b) f(100), and (c) f(800). (d) At the end of how
many days was half of the group discharged?
Part five:
Find the function values for each function:
 G(x)=|x-3|; g(10), g(3), g(-3)
 F(x)= 4 if x≥0
3 if x<0
F (3), F (-4), F (0)
Part six:
State (a) degree and (b) the leading coefficient of the given polynomial:
F(x)=7x3
-2x2
+6
3
200
200
1)( 







t
tf

5. Part seven:
Word problems:
 A coffeehouse sells a pound of coffee for $9.75. Expenses are $4500
each month, plus $4.25 for each pound of coffee sold.
a) Write a function r(x) for the total monthly revenue as a
function of the number of pounds of coffee sold.
b) Write a function e(x) for the total monthly expenses as a
function of the number of pounds of coffee sold.
c) Write a function (r - e) (x) for the total monthly profit as a
function of the number of pounds of coffee sold.
 Suppose the yearly demand function for a particular actor to star
in a film is p =
q
1200000
, where q is the number of films he stars in
during the year. If the actor currently charges $600,000 per film,
how many films does he star in each year? If he wants to star in
four films per year, what should his price be?
 Train Ride. A return train ticket between Rabat and
Mohammedia costs $6.24. Write the cost of a return ticket as a
function of a passenger’s income. What kind of function is this?
 Investment. If a principal of P dollars is invested at a simple
annual interest rate of r for t years, express the total accumulated
amount of the principal and interest as a function of t. Is your
result a linear function of t?

6. Part eight:
Solve the following composite function:
If F (t) = t2
+7t+1 and G (t) =
1
2
t
, find (FG) (t) and (GF) (t).
Part nine:
Word problem:
 Business. A manufacturer determines that the total number of
units of output per day, q, is a function of the number of
employees, m, where
The total revenue r that is received for selling q units is given by
the function g, where r = g(q) = 40q. Find (gof)(m). What does this
composite function describe?
4
)40(
)(
2
mm
mfq

