Class notes MAT421

TOPIC 1:
FUNCTIONS,
LIMITS &
CONTINUITY

, 1. FUNCTIONS
1. Properties ofFunctions
2. Operations onfunctions
3. Graphs offunctions
OUTLINES 2. LIMITS
1. Introduction
TOPIC 1 Functions and Limits
2. One-sided & Two sidedlimits
3. Computing limits
4. Computing limits: end
behaviour
3. CONTINUITY
1. Continuity at a point
2. Limits and continuity of
trigonometric functions

,1.1 FUNCTIONS 1. Properties of Functions
2. Operations on functions
3. Graphs of functions




LEARNING OBJECTIVES
At the end of this topic, students should be able to:
• Understand all the properties of Functions and know the
purpose of using it
• Learn how to find and solve the operation on functions
• Find limit of function at infinity and function when approach to
real numbers

, INTRODUCTION
Definition 1.1.1. domain range

▪ If a variable y depends on a variable x in
a such a way that each value of x
determines exactly one value of y, then we A function ( √ )

say that: y is a function of x domain range


Def 1.1.2.
▪ A function f is a rule that associates a
Not a function (×)
unique output with each input
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