3Tvwo §9.3 Fractional functions

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• Leerjaar 3

§9.3 Fractional functions

We start with an example!

This is a special table.

If x = 2  is   MULTIPLIED by 5 you get 10, then y = 25 is DIVIDED by 5 and so it becomes  5. 

   One more time:

If x = 1  is   MULTIPLIED by 4 you get 4 ,   then y = 50 is DIVIDED by 4 so it becomes 12.5

What a typical pattern, isn't it?         

There is another pattern as far as calculations from this table are concerned.

Write down  2 or 3 short calculations from the table, that all give the same outcome!

Remember them carefully and key in your findings in the next slide!

2 or 3 calculations with the same outcome:

5 multiplications (products) with the same outcome:

Because the product is 50 all the time, you can turn this

into a formula. This formula can have 3 different forms:

We call this an 'INVERSELY PROPORTIONAL' 

relation.

Question: What is 'INVERSELY PROPORTIONAL'  called in Dutch? 

KEY IN in the

next slide!

inversely proportional
is in Dutch: .......

^{In words:              Inversely proportional is:}

^{'omgekeerd evenredig' in Dutch.}

Task:

Write as two other formulas (the point means 'times'):

a⋅b=15

a⋅b=15

means the same as
(2 other formulas!):

Solution:

means the same as:                                 or:

a⋅b=15

a=​b​​15​​

b=​a​​15​​

'c is a constant number', it says above. You might wonder: aren't  x and y 

constants too? Well no, x and y are VARIABLES. This means they vary in value.

However c is the same value all the time!

Here follows an example, where c = 50 :

For your good understanding:

This is 

+  an inversely proportional relation and easily changed into:

+ a fractional function, too!

y=​x​​50​​

Functions have come back!

(I wonder if you missed them anyway...)

When we change y = 

into   f(    ) = 

we turn it into a FUNCTION!

​x​​4​​

x

​x​​4​​

​x​​3​​

​x​​3​​

GRAPHS ........

You might wonder by now:

What does the GRAPH for: 

f(    ) =                  look like? Next slide shows you the remarkable shape it has!

​x​​3​​

x

Awesome, isn't it?

A good explanation about this graph is given in the  Movie from the next slide!

+ This LessonUp I will share with you, so that

+ You can watch this Feelgood Movie later, 

+ Pausing whenever you like

By the way....

+ I hope it is all clear to you now

+ If not, by doing §9.3 by yourself and every little step you

    take, leads to the same content as we have just seen.

    The memory of whatever you've picked up now will help you, doing 

    §9.3 now!

Let's stay together for a while.

+ I ask you to start right now,

   doing §9.3

+ by staying a little longer,

   you can ask me questions by:

    a. mike

    b. chat

    c. mail

Homework time

§ 9.3 Fractional functions

You may skip:

+ Introduction p.62, on top

+ exercise 19

+ do not skip the Theory, p.62!

+ Hand in pics of your Homewerk on GoogleClassroom.