types of functions 05272011
TRANSCRIPT
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Welcome Back to School and Good
Morning!!
Have a nice day everyone!!!!
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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