FUNCTIONS powerpoint presentation example

OBJECTIVES:
 Define functions;
 Determine the domain and range of a
function;
 Illustrate functions using ordered pairs, table
of values, graphs, equations, and real-life
situations; and
 Represents real-life situations using functions.

Definition of a
Function
It is a relation define as a set of
ordered pairs (x, y) where no two or
more distinct ordered pairs have the
same first element (x).

Relation versus
Function
 Is a rule that
relates values called
the domain to a
second set of values
called range.
 Is a relation where
each element in the
domain is related to
only one value in
the range by some
rule.

One – to – One
Function
 every element of the domain has a
distinct image or co-domain element for
the given function.
 is also called an injective function.

Many – to – One
Function
 defined by more than one element of
the set A are connected to the same
element in the set B.
it is also called a constant function.

Onto Function
 that every element in set B has a pre-
image in set A.
is also called a subjective function.

Into Function
 is exactly opposite in properties to an
onto function.
 there are certain elements in the co-
domain that do not have any pre-image.

Examples:
Determine whether the following given is
function or not function.
Function Function

Examples:
Determine whether the following given is
function or not function.
Function
Not a Function

A function can be described
by:
Ordered Pairs
 It is a composition of the domain and
the range having two values written
in a fixed order within the
parenthesis.

g = {(-3,3), (-2,-6), (-1,0), (0, 15), (3, 2)}
t = {(1,0), (4,2), (3,5), (1,9), (5,7)}
g = {(-3,3), (-2,-6), (-1,0), (0, 15), (3, 2)}
t = {(1,0), (4,2), (3,5), (1,9), (5,7)}
Function
Not a Function

by:
Table of Values
 This shows the correspondence
between a set of values of x and a
set of values y in a tabular form.

x Mother Sister Aunt
y Father Brother Uncle
X -6 -1 -1 7
Y 2 -1 4 4
Function
X -6 -1 -1 7
Y 2 -1 4 4
Not a Function

by:
Mapping Diagram
 It is like a flow chart for functions, showing
the input (x) and output (y) values. A
mapping diagram consists of two parallel
columns and arrows that are drawn from
domain and range, to represent the relation
between two elements.

by:
Graphs
 A diagram represents the variation of a variable
in comparison to one or more two variables.
*** You can use the vertical line test to determine if
a graph is a function or not. In this method, if a
vertical line intersects the graph in all places at
exactly one point, then the relation is a function.

Function
Not a Function
Function

by:
Functions in Real – Life
In the real world, functions are mathematical
representations of many input-output
situations.

o{person, social security number}
Function
o{height, student}
Not a Function
o{student, id number}
Function

Lesson 2:
Domain and
Range
of a Function

Two Important Elements of a
Function
DOMAIN
 it is a set of all x –
coordinates in the
set of ordered pairs.
 It is also called as
input.
RANGE
 it is a set of all y –
coordinates in the
set of ordered pairs.
 It is also called as
output.

X Y
Domain (D): {a, b, c}
Range (R): {1, 2, 3}

Domain (D): {-3, -2, -1, 0, 1}
Range (R): {-6}
Determine the domain and
range of

Domain (D): {-1, 0, 1, 2, 3}
Range (R): {3, 5, 11, 21}
range of

x -1 -2 -3 4 5
y 0 1 2 3 3
Domain (D): {-1, -2, -3, 4, 5}
Range (R): {0, 1, 2, 3}
Determine the domain and range of

ACTIVITY: 2
Determine the domain and range of a
function.
1. 3.
4. {(2, 5), (4, 8), (-1, 7), (-4, -3)}
2. 5. {(2, -4), (4, 7), (-1, -4), (2, -7),
(0, -7), (3, 6)}
x 0 4 5 4 7
y -3 0 -1 2 2

Piecewise
Functions
 These are functions which are
defined in different domains
since they are determined by
several equations.

𝒇 (𝒙)={−𝒙 +𝟏,𝒊𝒇 𝒙<𝟑
𝟑 𝒙 −𝟐,𝒊𝒇 𝒙 ≥𝟑
range of

range of
𝒇 (𝒙)=
{−𝟐 𝒙−𝟏,𝒊𝒇 𝒙>𝟐
𝟐 𝒙−𝟗,𝒊𝒇 𝒙≤𝟐

Determine the domain and range of.
Give at least 3 values in each
equation.
𝒇 (𝒙)=
{ 𝟑𝒙−𝟔,𝒊𝒇 𝒙>𝟒
𝟔𝒙
𝟐
+𝟐𝒙−𝟒,𝒊𝒇 𝒙 ≤𝟐
ACTIVITY: 3

Evaluating function means finding the
value of f(x) that corresponds to a
given value of x.

Example 1:
Evaluate the function if
Solution:

Example 2:
Solution:

Example 3:
Solution:

ACTIVITY:4
Solve the problem in function machine.
1. If -2 goes into the machine, what number comes out?
2. If 6 goes into the machine, what number comes out?
3. If 0 goes into the machine, what number comes out?
4. If 4x goes into the machine, what comes out?
5. If -5 goes into the machine, what comes out?

OBJECTIVES:
•Define operations on functions;
and
•Solve problems involving
operation on functions.

Addition of
Functions
Given the function and with
domains A and B respectively the
sum of the functions is

Example 1:
Given the following functions
find :

Example 2:
find :

Example 3:
find :

Example 4:
find :

Given two functions their
difference denoted by , is the
function defined by
Subtraction of Functions

Multiplication of
Functions
Denoted by , is the function
defined by

Example 1:
;
Find:

FOIL METHOD
F – first
O – outer
I – Inner
L - Last

Example 2:
Find:

Example 3:

Division of Functions
Denoted by , is the function
defined by

Factoring Polynomials
●Factoring is the process of finding the
factors of a number or polynomial. It
is the simplest way to solve equations
of a higher degree. Although you
should already be proficient in
factoring, here are the methods you
should be familiar with, in case you
need to review.

●Factoring Difference of Two
Squares
●Factoring Perfect Square Trinomial
●Factoring General Trinomial

Factoring Difference of
Two Squares

The difference of the two squares is the
most common. This form is very easy to
identify. Whenever you have a binomial
term and they have subtraction as the
middle sign, you are guaranteed to have
the case of difference of two squares.
Difference of Two Squares (DTS)

The formula for Difference of Two
Squares:

Factoring Perfect Square
Trinomials
(PST)

Perfect Square Trinomials
(PST)
A perfect square trinomial is the square
of a binomial. It follows a pattern when
it is factored so that the first and last
terms are perfect squares of monomials
and the middle term is twice their
product.

Examples:
Factor
Factor
Factor
Factor

Example 1:
and
Find:

Factoring General Trinomials
It is an algebraic expression made
up of three terms. The general
form of a quadratic trinomial is
written as
where a, b, and c are constants.

Example 1:
Factor the trinomial

Example 2:

Example 3:

Example 4:

Example 2:
and
Find:

Example 3:
Find:

Example 4:
Find:

Activity:
Factor the following
polynomials
1)
2)
3)
4)
5)

Activity:
Factor the following
polynomials
6)
7)
8)
9)
10)

FUNCTIONS powerpoint presentation example

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