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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 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.

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Слайд 1
Made by ALEXP1 Chapter 3«Functions and combining functions»
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Made by ALEX

P1 Chapter 3

«Functions and combining functions»


Слайд 3
A few of the possible values of xWe can illustrate a function with a
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A few of the possible values of x

We can illustrate a function with a diagram

The rule is sometimes called a mapping.



Слайд 4
We say “ real ” values because there is a branch of mathematics which
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We say “ real ” values 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 the domain and which the range, notice that
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Tip: To help remember which is 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 the domain and which the range, notice that
Текст слайда:

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



Слайд 8
Solution: The quickest way to sketch this quadratic function is to find its vertex
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Solution: The quickest way to sketch this quadratic function is to find its vertex by completing the square.



Слайд 9
The x-values on the part of the graph
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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:
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so the graph is:



Слайд 11
SUMMARY
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SUMMARY



Слайд 12
ExerciseFor each function write down the domain and range 1.	Sketch the functions
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Exercise

For each function write down the domain and range

1. Sketch the functions where

Solution:



Слайд 13
So, the domain isWe can sometimes spot the domain and range of a function
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So, the domain is

We can sometimes 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 Functionx is replaced by 3
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Functions of a Function

x is replaced by 3


Слайд 15
Suppose        andFunctions of a Functionx is replaced by −1
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Suppose and

Functions of a Function

x is replaced by −1


Слайд 16
andSuppose        andx is “operated” on by the
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and

Suppose and

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


Functions of a Function


Слайд 17
Notation for a Function of a FunctionWhen we meet this notation it is a
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Notation for a Function of a Function

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



Слайд 18
Solution:
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Solution:


Слайд 19
e.g. 1 Given that         and
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e.g. 1 Given that and find

Solution:


Слайд 20
Solution:e.g. 1 Given that         and
Текст слайда:

Solution:

e.g. 1 Given that and find


Слайд 21
Solution:e.g. 1 Given that         and
Текст слайда:

Solution:

e.g. 1 Given that and find


Слайд 22
Solution:e.g. 1 Given that         and
Текст слайда:

Solution:

e.g. 1 Given that and find


Слайд 23
Solution:e.g. 1 Given that         and
Текст слайда:

Solution:

e.g. 1 Given that and find


Слайд 24
Solution:e.g. 1 Given that         and
Текст слайда:

Solution:

e.g. 1 Given that and find


Слайд 25
Solution:e.g. 1 Given that         and
Текст слайда:

Solution:

e.g. 1 Given that and find


Слайд 26
Solution:e.g. 1 Given that         and
Текст слайда:

Solution:

e.g. 1 Given that and find


Слайд 27
Solution:e.g. 1 Given that         and
Текст слайда:

Solution:

e.g. 1 Given that and find


Слайд 28
Solution:e.g. 1 Given that         and
Текст слайда:

Solution:

e.g. 1 Given that and find


Слайд 29
Solution:e.g. 1 Given that         and
Текст слайда:

Solution:

e.g. 1 Given that and find

e.g. 1 Given that and find


Слайд 30
Solution:e.g. 1 Given that         and
Текст слайда:

Solution:

e.g. 1 Given that and find

e.g. 1 Given that and find



Слайд 31
Exercise1. The functions f and g are defined as follows:(a) What is the range
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Exercise

1. The functions f and g are defined as follows:

(a) What is the range of f ?



Слайд 32
Periodic FunctionsFunctions whose graphs have sections which repeat are called periodic functions.e.g.This has a
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Periodic Functions

Functions whose graphs have sections which repeat are called periodic functions.

e.g.

This has a period of 3.



Слайд 33
Even functions are symmetrical about the y - axise.g.
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Even functions are symmetrical about the y - axis

e.g.



Слайд 34
Odd functions have 180° rotational symmetry about the origine.g.
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Odd functions have 180° rotational symmetry about the origin

e.g.



Слайд 35
Try to sketch one even function, one odd and one that is neither. Ask
Текст слайда:

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



Слайд 36
SUMMARYA compound function is a function of a function.
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SUMMARY

A compound function is a function of a function.