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Презентация на тему по математике Функции, 10 класс

A few of the possible values of xWe can illustrate a function with a diagram The rule is sometimes called a mapping.
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 2


Слайд 3 A few of the possible values of x
We

A few of the possible values of xWe can illustrate a

can illustrate a function with a diagram
The rule

is sometimes called a mapping.



Слайд 4 We say “ real ” values because there

We say “ real ” values because there is a branch

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

Tip: To help remember which is the domain and which the

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

Tip: To help remember which is the domain and which the

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

Solution: The quickest way to sketch this quadratic function is to

function is to find its vertex by completing the

square.



Слайд 9 The x-values

The x-values on the part of the graph

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 domain and

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

range
1. Sketch the functions

where

Solution:



Слайд 13 So, the domain is
We can sometimes spot the

So, the domain isWe can sometimes spot the domain and range

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 by 3

Functions of a Functionx is replaced 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” on by the inner function first.Functions of a Function

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

Functions

of a Function

Слайд 17 Notation for a Function of a Function
When we

Notation for a Function of a FunctionWhen we meet this notation

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:

and

find

Solution:


Слайд 20 Solution:
e.g. 1 Given that

Solution:e.g. 1 Given that     and    find

and

find

Слайд 21 Solution:
e.g. 1 Given that

Solution:e.g. 1 Given that     and    find

and

find

Слайд 22 Solution:
e.g. 1 Given that

Solution:e.g. 1 Given that     and    find

and

find

Слайд 23 Solution:
e.g. 1 Given that

Solution:e.g. 1 Given that     and    find

and

find

Слайд 24 Solution:
e.g. 1 Given that

Solution:e.g. 1 Given that     and    find

and

find

Слайд 25 Solution:
e.g. 1 Given that

Solution:e.g. 1 Given that     and    find

and

find

Слайд 26 Solution:
e.g. 1 Given that

Solution:e.g. 1 Given that     and    find

and

find

Слайд 27 Solution:
e.g. 1 Given that

Solution:e.g. 1 Given that     and    find

and

find

Слайд 28 Solution:
e.g. 1 Given that

Solution:e.g. 1 Given that     and    find

and

find

Слайд 29 Solution:
e.g. 1 Given that

Solution:e.g. 1 Given that     and

and

find

e.g. 1 Given that and find


Слайд 30 Solution:
e.g. 1 Given that

Solution:e.g. 1 Given that     and

and

find

e.g. 1 Given that and find



Слайд 31 Exercise
1. The functions f and g are defined

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

as follows:
(a) What is the range of f ?


Слайд 32 Periodic Functions
Functions whose graphs have sections which repeat

Periodic FunctionsFunctions whose graphs have sections which repeat are called periodic

are called periodic functions.
e.g.
This has a period of 3.


Слайд 33 Even functions are symmetrical about the y -

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

axis
e.g.


Слайд 34 Odd functions have 180° rotational symmetry about the

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

origin
e.g.


Слайд 35 Try to sketch one even function, one odd

Try to sketch one even function, one odd and one that

and one that is neither. Ask your partner to

check.



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