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Презентация, доклад по математике Функции, 10 класс

Презентация на тему Презентация по математике Функции, 10 класс, из раздела: Алгебра. Эта презентация содержит 36 слайда(ов). Информативные слайды и изображения помогут Вам заинтересовать аудиторию. Скачать конспект-презентацию на данную тему можно внизу страницы, поделившись ссылкой с помощью социальных кнопок. Также можно добавить наш сайт презентаций в закладки! Презентации взяты из открытого доступа или загружены их авторами, администрация сайта не отвечает за достоверность информации в них. Все права принадлежат авторам презентаций.

Made by ALEXP1 Chapter 3«Functions and combining functions» A few of the possible values of xWe can illustrate a function We say “ real ” values because there is a branch of Tip: To help remember which is the domain and which the range, Tip: To help remember which is the domain and which the range, Solution: The quickest way to sketch this quadratic function is to find The x-values on the part of so the graph is: SUMMARY ExerciseFor each function write down the domain and range 1.	Sketch the functions So, the domain isWe can sometimes spot the domain and range of Functions of a Functionx is replaced by 3 Suppose        andFunctions of a Functionx is replaced by −1 andSuppose        andx is “operated” on Notation for a Function of a FunctionWhen we meet this notation it Solution: e.g. 1 Given that Solution:e.g. 1 Given that Solution:e.g. 1 Given that Solution:e.g. 1 Given that Solution:e.g. 1 Given that Solution:e.g. 1 Given that Solution:e.g. 1 Given that Solution:e.g. 1 Given that Solution:e.g. 1 Given that Solution:e.g. 1 Given that Solution:e.g. 1 Given that Solution:e.g. 1 Given that Exercise1. The functions f and g are defined as follows:(a) What is Periodic FunctionsFunctions whose graphs have sections which repeat are called periodic functions.e.g.This Even functions are symmetrical about the y - axise.g. Odd functions have 180° rotational symmetry about the origine.g. Try to sketch one even function, one odd and one that is SUMMARYA compound function is a function of a function.
Слайды презентации

Слайд 1 Made by ALEX
P1 Chapter 3
«Functions and

Made by ALEXP1 Chapter 3«Functions and combining functions» combining functions»

Слайд 2


Слайд 3 A few of the possible values

A few of the possible values of xWe can illustrate a of x

We can illustrate a function with a diagram

The rule is sometimes called a mapping.



Слайд 4 We say “ real ” values

We say “ real ” values because there is a branch because there is a branch of mathematics which deals with numbers that are not real.

A bit more jargon

To define a function fully, we need to know the values of x that can be used.



Слайд 5 Tip: To help remember which is

Tip: To help remember which is the domain and which the the domain and which the range, notice that d comes before r in the alphabet and x comes before y.

Слайд 6 Tip: To help remember which is

Tip: To help remember which is the domain and which the the domain and which the range, notice that d comes before r in the alphabet and x comes before y.



Слайд 7


Слайд 8 Solution: The quickest way to sketch

Solution: The quickest way to sketch this quadratic function is to this quadratic function is to find its vertex by completing the square.



Слайд 9

The x-values on the part The x-values on the part of the graph we’ve sketched go from −5 to +1 . . .

BUT we could have drawn the sketch for any values of x.

( y is any real number greater than, or equal to, −5 )

BUT there are no y-values less than −5, . . .

domain:



Слайд 10 so the graph is:

so the graph is:

Слайд 11 SUMMARY

SUMMARY

Слайд 12 Exercise
For each function write down the

ExerciseFor each function write down the domain and range 1.	Sketch the domain and range

1. Sketch the functions where

Solution:



Слайд 13 So, the domain is
We can sometimes

So, the domain isWe can sometimes spot the domain and range spot the domain and range of a function without a sketch.

x + 3 must be greater than or equal to zero.

Other values are greater than zero.

So, the range is



Слайд 14 Functions of a Function
x is replaced

Functions of a Functionx is replaced by 3 by 3

Слайд 15 Suppose

Suppose        andFunctions of a Functionx is replaced by −1 and

Functions of a Function

x is replaced by −1


Слайд 16 and
Suppose

andSuppose        andx is “operated” and

x is “operated” on by the inner function first.


Functions of a Function


Слайд 17 Notation for a Function of a

Notation for a Function of a FunctionWhen we meet this notation Function

When we meet this notation it is a good idea to change it to the full notation.



Слайд 18 Solution:

Solution:

Слайд 19 e.g. 1 Given that

e.g. 1 Given that and find

Solution:


Слайд 20 Solution:
e.g. 1 Given that

Solution:e.g. 1 Given that and find

Слайд 21 Solution:
e.g. 1 Given that

Solution:e.g. 1 Given that and find

Слайд 22 Solution:
e.g. 1 Given that

Solution:e.g. 1 Given that and find

Слайд 23 Solution:
e.g. 1 Given that

Solution:e.g. 1 Given that and find

Слайд 24 Solution:
e.g. 1 Given that

Solution:e.g. 1 Given that and find

Слайд 25 Solution:
e.g. 1 Given that

Solution:e.g. 1 Given that and find

Слайд 26 Solution:
e.g. 1 Given that

Solution:e.g. 1 Given that and find

Слайд 27 Solution:
e.g. 1 Given that

Solution:e.g. 1 Given that and find

Слайд 28 Solution:
e.g. 1 Given that

Solution:e.g. 1 Given that and find

Слайд 29 Solution:
e.g. 1 Given that

Solution:e.g. 1 Given that and find

e.g. 1 Given that and find


Слайд 30 Solution:
e.g. 1 Given that

Solution:e.g. 1 Given that and find

e.g. 1 Given that and find



Слайд 31 Exercise
1. The functions f and g

Exercise1. The functions f and g are defined as follows:(a) What are defined as follows:

(a) What is the range of f ?



Слайд 32 Periodic Functions
Functions whose graphs have sections

Periodic FunctionsFunctions whose graphs have sections which repeat are called periodic which repeat are called periodic functions.

e.g.

This has a period of 3.



Слайд 33 Even functions are symmetrical about the

Even functions are symmetrical about the y - axise.g. y - axis

e.g.



Слайд 34 Odd functions have 180° rotational symmetry

Odd functions have 180° rotational symmetry about the origine.g. about the origin

e.g.



Слайд 35 Try to sketch one even function,

Try to sketch one even function, one odd and one that one odd and one that is neither. Ask your partner to check.



Слайд 36 SUMMARY
A compound function is a function

SUMMARYA compound function is a function of a function. of a function.