Guc 2029 61 37611 2023-10-29T18 28 36
Guc 2029 61 37611 2023-10-29T18 28 36
Guc 2029 61 37611 2023-10-29T18 28 36
Mathematics
For Business Informatics (MATH-105)
Assignment Nr. 1
Name: ID: .
a) 𝒚𝟐 = 𝒙 − 𝟑
b) 𝒚 = −𝒙𝟒 + 𝟕
a) 𝒚 = 𝒙 − 𝟑
b) 𝒚 = −𝒙𝟒 + 𝟕
c) 𝒇(𝒙) = −𝒙𝟑 − 𝒙
Exercise 3: Decide from the graph whether the following Functions are even, odd or neither nor;
𝟐𝒙
b) −𝟑 ≤ 𝟏 − ≤𝟑
𝟓
c) |𝟑𝒙 + 𝟒| = |𝟐𝒙 + 𝟔|
d) (𝒙 − 𝟒)𝟐 = 𝟗 "𝒕𝒂𝒌𝒆 𝒔𝒒𝒖𝒂𝒓𝒆 𝒓𝒐𝒐𝒕 𝒃𝒐𝒕𝒉 𝒔𝒊𝒅𝒆𝒔 𝒂𝒏𝒅 𝒓𝒆𝒄𝒂𝒍𝒍 𝒕𝒉𝒂𝒕 √𝒙𝟐 = |𝒙| = ±𝒙 "
e) 𝟑(𝟒 − 𝐲) ≥ 𝟗
(j)
Exercise 6:
1- If a function is defined by:
𝑥, 𝑥<0
𝒇(𝒙) = { 𝑥2 , 0<𝑥≤2
8 − 𝑥, 𝑥>2
Evaluate:
Exercise 7:
(Linear Depreciation = the same amount is depreciated every year from the equipment’s value)
A small business purchased a piece of equipment for $1000. After 4 years the equipment will be
outdated, having no value.
(a) Construct a linear model (linear equation) giving the value 𝒚 of the equipment in terms of the
time 𝒕 in years, 𝟎 ≤ 𝒕 ≤ 𝟒.
(b) What is the value of the equipment after 2 years?
(c) Find the time when the value of the equipment will be $550.
Exercise 8:
Find the slope and 𝒚 −intercept of the following straight line, and then graph the line:
−𝒙 + 𝟐𝒚 = 𝟔
Exercise 9:
Find the limit (if exists):
𝟑
𝒂) 𝐥𝐢𝐦 √𝒙 + 𝟐
𝒙→𝟐
|𝒙 − 𝟖|
𝒃) 𝐥𝐢𝐦
𝒙→𝟖 𝒙 − 𝟖
𝟏
( ) 𝒚−𝟓 𝒚≤𝟐
𝒄) 𝐥𝐢𝐦 𝒇(𝒚) , 𝐰𝐡𝐞𝐫𝐞 𝒇 𝒚 = { 𝟐
𝒚→𝟐
−𝟑𝒚 + 𝟒 𝒚>𝟐
Exercise 10:
Discuss the continuity of the following function at the given point:
𝟐𝒙
𝒇(𝒙) = 𝐚𝐭 𝒙 = −𝟐 𝐚𝐧𝐝 𝐚𝐭 𝒙 = −𝟔
𝒙𝟐 − 𝟒𝒙 − 𝟏𝟐
𝟑 − 𝒙, 𝒙<𝟐
𝒇(𝒙) = { 𝒙 𝐚𝐭 𝒙 = 𝟐, 𝒙 = 𝟓 𝐚𝐧𝐝 𝐚𝐭 𝒙 = −𝟑
, 𝒙>𝟐
𝟐
𝐕𝐢𝐞𝐥 𝐄𝐫𝐟𝐨𝐥𝐠!
5/5 Math-105 Assign-1