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Types of Functions and

Some Special Functions

By: Mr. Boyet B. Aluan

???Questions?????

????

1. What are the kinds of function?

2. How can we differentiate one function from another?

TYPES OF FUNCTION AND SOME SPECIAL FUNCTION

Constant Functions- assigns the same real number to every element of the domain. This function contains only the constant term. It is of the form f(x) =0x +c or f(x)= c such as f(x)= 8. It is generally a horizontal line.

LINEAR FUNCTIONS-

if the degree of the polynomial function is 1 then it is a linear function. It is generally define by the equation

f(x)= mx+b. Using 5x+y = 4. The equation can be rename as y = -5x +4 so that we can give value of x and y and then its graph.

x

y

x

yQUADRATIC FUNCTION

a polynomial with second degree. This function is define by f(x)= Types of quadratic relations are:

, ,

Circles:Ellipse

hyperbola

Parabola

POWER/CUBIC FUNCTIONS –

– it is a polynomial functions with 3rd degree define by f( ). A cubic relation is a cubic function because there’s only one range for every value of domain. This is illustrated by y= f(x)=

x

y

IDENTITY FUNCTIONS

it is define by f(x)= x, or y= x. where each element of the domain onto itself.

x

y

ABSOLUTE VALUE FUNCTIONS

contains the absolute value of a quantity, such as f(x) = |x|. It can be define as follows f(x)= x, x>0, f(x)= 0, x=0,f(x)= -x, x= <0.

x

y

RATIONAL FUNCTIONS-

a function expressed as the quotient of two polynomial functions. Example. .

.

4

12

23

x

xx

ALGEBRAIC FUNCTIONS

the function formed by a finite number of algebraic operations on the identity function and the constant function. The algebraic operations

include four fundamental operations, raising to powers, and extracting square roots. Example:

1

122

22

x

xx

GROUP ACTIVITY

Be cooperativeWork as a teamAlways read and understand rules and procedures

Strictly follow the instructionsBEHAVEBe aware of time limits!

TELLING COMPETITION:

Group 1: x -2 -1 0 1 2

y 4 1 0 1 4

Refer to Quadratic function

TELLING COMPETITION:

Group 2:

3xxf

Refer to Cubic Functions

TELLING COMPETITION:

Group :3

6333 yx

Refer to Linear function-27

6

TELLING COMPETITION:

Group 4:

4xf

Refer to Constant Functions

4

TELLING COMPETITION:

Group 5:

22xxf

Refer to Quadratic Function

4

???Questions?????

????2. How can we

differentiate one function from another?

Summary!

DO THIS!!!! 10-POINTS

Write a letter to your friend and discuss “The types of Functions and some Special Function” to the manner that you are giving menu for a

recipe.

Points Description

10 Writes a clearly stated main idea, topic and presents supporting details in a logical order. The journal is written with correct use of conventions (grammar, punctuation, capitalization, and spelling)

8Writes clearly stated main idea, topic and presents supporting details in a logical order. The details may not be as complete as it could be. The journal is written with generally correct use of conventions.

6Writes a clearly stated main idea, topic but presents some unrelated details. There are few errors in the use of conventions.

4 Writes a main idea, topic but not clearly stated. Details may not be presented in a logical order, or some of the information may be inaccurate. The journal may include some errors in the use of conventions.

2 No accurate understanding of topic/subject.

TO DOS’

Make a research of at least three different graphs that shows the types of functions. E.g Sciences, Economics, Psychology, Statistics.

T h a n k Y o u a n d G o o d B y e!!!

BY:

Mr. Boyet Bandoja Aluan