MAT 1318 Supplemental Exam
Winter 2010
Instructor: Charles Starling
Q
Family Name:
First Name:
Student Number:
A
Score
1
2
3
PLEASE READ THESE INSTRUCTIONS VERY
CAREFULLY.
4
5
1. You have 3 hours to complete this exam.
2. This is a closed book exam, and n
MAT1318X - Assignment 1 - Summer 2012 - Instructor Charles Starling
This assignment must be printed out and lled in and is due July 13.
Student Number:
Name:
1. Reply true or false:
4
4
4
(a) =
=
7
7
7
1
2
(b)
2
.
12
=
(2)2
(c)
(d)
5 3
=2
6 5
(i)
.
1+1=
3
3.1
Polynomial and Rational Functions
Polynomial Functions and their Graphs
So far, we have learned how to graph polynomials of degree 0, 1, and 2. Degree 0 polynomial
functions are things like f (x) = 2, which is a straight horizontal line with constan
2
FUNCTIONS
2
26
Functions
2.1
What is a Function?
Denition 2.1 A function is a rule that assigns to each element x in a set A exactly one
element, called f (x), in a set B. Here the set A is called the domain of the function. We
will also write
f :AB
So
6
Trigonometric Functions of Angles
6.1
Angle Measures
When we think of measuring angles, the unit we usually think of is degrees. A right
angle is 90 , a straight angle is 180 and so on. When talking about angles in the plane, we
measure them countercloc
5
5.1
Trigonometric Functions
The Unit Circle
Denition 5.1 The unit circle is the circle of radius 1 centered at the origin in the xyplane:
x2 + y 2 = 1
Example: The point P
3
, 36
3
3
3
is on the unit circle because
2
+
6
3
2
=
3 6
9
+ = =1
9 9
9
Termina
7
Analytic Trigonometry
7.1
Trigonometric Identities
Lets begin by listing the identities we already know.
Reciprocal Identities:
1
sin
sec =
1
cos
cot =
tan =
csc =
sin
cos
cot =
1
tan
cos
sin
Pythagorean Identities:
sin2 + cos2 = 1
tan2 + 1 = sec
4
Exponential and Logarithmic Functions
4.1
Exponential Functions
Denition 4.1 If a > 0 and a = 1, then the exponential function with base a is given
by f (x) = ax .
Examples: f (x) = 2x , g(x) = 10x , h(x) =
1
3
x
.
Graphs of Exponential Functions
Exampl