TUTORIAL 2
231
Note: for this question at least one x-value must not be assigned a y-value.
(c): One possible table is
x 1 2 3 4 4
y 2 4 6 8 10
The co-domain is A = cfw_2, 4, 6, 8, 10.
We have dom(f ) = B = cfw_1, 2, 3, 4 and range(f ) = cfw_2, 4, 6, 8, 1

'2 Exercises
1 .
1
In-Exercises 16, ll in the blanks.
.1. The set of all real numbers that are solutions of an
inequality is the of the inequality.
2. The set of all points on the real number line that
represents the solution set of an inequality is the

CHAPTER 10
Tutorials
Problems in a shaded box are those that are assessed problems and it is required that these be
completed for the full 10% tutorial participation mark to be awarded. Completion of these questions
will provide a rudimentary knowledge bu

Unit Outline
MCD2130
Functions and their
Applications
Diploma of Business
Monash College Diploma
Unit Outline
Diploma of Business
Contents
Description . 2
Objectives . 2
Language Outcomes . 2
Learning and Teaching . 3
Unit Schedule . 6
Assessment & Feedba

Solving Inequalities
Larson Section P2 (p15)
An equation is a mathematical statement containing =
An inequation is mathematical statement containing any of <, >, ,
Solving an inequality means finding all values of x that make that statement
true.
Linear

MCD2130
MCD2130 Tutorial Week 1
1. Yes
2.
Shaded Tutorial Problems
Week 2
Solutions
3. False
5.
(a)
(b)
(c)
(d)
8. (a) f ( 2 ) = 5
(b) There is no x for which f ( x ) = 0
(c) You can solve y = x 2 + 1 if and only if y [1, ) .
9. (a) D f = R \cfw_8
5 5
(

MCD2130
MCD2130 Tutorial Week 1
Shaded Tutorial Problems
Week 3
Solutions
2. (a) ( 3 f + 4 g )( 2 ) = 32
f +g
(b)
( 2 ) = 1
gh
4.
1
(b) dom = (1, 2 ) ( 2, 4]
fg
6. (a)
h o g o g ( x ) = 1 2x + x2
(b)
dom ( h o g o g ) = \ cfw_0
(c)
h o g o g (1)

TUTORIAL 3
208
Tutorial 3
Before attending your allocated tutorial class read the following:
The lecture notes, and
Larson et.al.
Section 1.2; pages 85-88. (Functions: Graphically)
Section 1.4; pages 107-111. (Combinations and compositions of function

CHAPTER 11
Tutorial Answers
Tutorial 1
4:
(a): (i) cfw_x R : 2 < x < 3, (ii) (2, 3) (iii) number line for this set is
0
4
3
2
0
1
0
1
2
3
x
4
(b): (i) cfw_x R : 0.75 < x 4, (ii) (0.75, 4] (iii) number line for this set is
0
4
3
2
1
0
0
1
2
3
x
4
7: Let A

CHAPTER 1
Set Theory
We will take an naive or intuitive view of set theory. For the purposes of this subject a set is a
collection of objects. A set is determined by the objects it contains. Objects in a set are called
elements of the set. Some elements i

TUTORIAL 4
253
TUTORIAL 4
254
TUTORIAL 4
257
12: Consider the composition function (h k g f )(x).
The composition
(g f )(x) = g(f (x)
= g x2
= 2x2
describes a dilation of y = x2 by a factor of 2 in the y-direction (away from the x-axis).
The composition
(

TUTORIAL 9
305
Tutorial 9
(1): Let = 0 and =
2
then
cos 0 +
2
= cos
2
=0
while
cos(0) + cos
2
=1+0
= 1.
Therefore cos 0 +
2
= cos(0) + cos
2
.
(2) : One way to determine this is
cos
(3):
= cos
12
4
3
= cos
4
3
= cos
cos
sin
sin
4
3
4
3
= cos
cos
+

332
TUTORIAL 12
Tutorial 12
(1):
d 1 x2 2
dF
=
e x 1
dx
dx 2
d 1 x2
1 2 d 2
e
x 1 + x2 1
= ex
2 dx
dx 2
1 2
1 2
2 d
= ex (2x) +
x 1 ex
x2
2
2
dx
1 2
1 2
2
x 1 ex (2x)
= ex (2x) +
2
2
3 x2
=x e .
Hence F is an antiderivative of f .
(2): (a):
1
x2 3x5 7 dx

1.2 Analyzing Graphs of Functions 93
i in the blanks. I In Exercises 13-16, use the graph of the function to nd
. fctionfiS the collection of :Ziiuggmam and range of f and the indicated function
r is used to determine 13- (a) f("2) ('30 f(_1) 14-. (a) f(