BUSM 5130PO3
Assignment #1
Solve the following 5 problems for this assignment. Questions are from the material that
we covered in class. Please complete the required information on the front page template
that I have posted on Moodle, print and include it in your assignment. Save your work as
pdf and upload it on Moodle. This assignment is due at the beginning of the class next
week. You can work in teams of 2-3 students in this assignment. Include the names and
student numbers of students who worked together to solve the problems. Please upload
only one file per team, if you work in a team.
1. Find the domain of the following functions:
8
a) 𝑓(𝑥) = 𝑥−2
(−∞,2)∪(2,∞)
b) 𝑓(𝑥) = 2√𝑥 − 1
[1,∞)
2. Consider the following matrix that has 4 rows and 7 columns. Using the double sum
notation, add cells in the highlighted part of the table.
= 𝑥23 + 𝑥24 + 𝑥25 + 𝑥26 + 𝑥34 + 𝑥35 + 𝑥36 + 𝑥44 + 𝑥45 + 𝑥46
3. A company that produces digital cameras in the USA has produced the following
price-demand data in table 1:
Table 1: Price-Demand
X Millions
2
5
8
12
P ($)
87
68
53
37
Using regression analysis, the company produced the following price-demand
function to model the above data:
𝑃(𝑥) = 94.8 − 5𝑥
𝑓𝑜𝑟 1 ≤ 𝑥 ≤ 15
a) Plot the data in table 1. Then sketch a graph of the price-demand function in the
same coordinate system.
b) What is the company’s revenue function for the cameras and what is its
domain?
c) Complete the following table. Then sketch a graph of the revenue function using
these points.
Revenue Table:
X Millions
1
3
6
9
12
15
a.) 𝑃(𝑥) = 94.8 − 5𝑥
P ($)
90
?
?
?
?
?
𝑓𝑜𝑟 1 ≤ 𝑥 ≤ 15
b.) Revenue Function
𝑅(𝑥) = 𝑥 ∙ 𝑃(𝑥)
𝑃(𝑥) = 94.8 − 5𝑥
𝑅(𝑥) = 𝑥(94.8 − 5𝑥) = 94.8𝑥 − 5𝑥 2
Domain: (−∞, ∞)
c.) Revenue Table
x (Millions)
R(x) ($)
1
89.8
3
239.4
6
388.8
9
448.2
12
417.6
15
297
4. Solve problem 2.1 on page 128 of the book.
1 − x2 ≥ 0
−1 ≤ x ≤ 1
Domain of f is [−1, 0) ∪ (0, 1]
𝑥2 + 1 ≠ 0
√𝑥 2 + 1 = 𝑥
𝑥2 + 1 = 𝑥2
1=0
Domain of g is the whole real line.
5. Solve problem 2.2 on page 128 of the book.
a.) y = mx + q
y = −3x + 10
b.) y − y0 = m(x − x0)
y − 4 = 5(x + 2)
y = 5x + 14
3−(−5)
c.) 𝑚 = 1−3 = −4
y − 3 = −4(x − 1)
y = −4x + 7