3Tvwo §9.3 Fractional functions

§9.3 Fractional functions
We start with an example!

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In deze les zitten 23 slides, met interactieve quizzen, tekstslides en 2 videos.

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§9.3 Fractional functions
We start with an example!

Slide 1 - Tekstslide

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?         

Slide 2 - Tekstslide

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!

Slide 3 - Tekstslide

2 or 3 calculations with the same outcome:

Slide 4 - Woordweb

5 multiplications (products) with the same outcome:

Slide 5 - Tekstslide

Because the product is 50 all the time, you can turn this
into a formula. This formula can have 3 different forms:

Slide 6 - Tekstslide

We call this an 'INVERSELY PROPORTIONAL' 
relation.
Question: What is 'INVERSELY PROPORTIONAL'  called in Dutch? 
KEY IN in the
next slide!

Slide 7 - Tekstslide

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

Slide 8 - Woordweb

In words:              Inversely proportional is:
'omgekeerd evenredig' in Dutch.

Slide 9 - Tekstslide

Task:
                                      Write as two other formulas :


ab=15

Slide 10 - Tekstslide

ab=15
means the same as
(2 other formulas!):

Slide 11 - Woordweb

Solution:


means the same as:                                 or:
ab=15
a=b15
b=a15

Slide 12 - Tekstslide

'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 :

Slide 13 - Tekstslide

Slide 14 - Tekstslide

For your good understanding:

This is 
+  an inversely proportional relation and easily changed into:
+ a fractional function, too!
y=x50

Slide 15 - Tekstslide

Functions have come back!
(I wonder if you missed them anyway...)
When we change y = 

into   f(    ) = 

we turn it into a FUNCTION!
x4
x
x4
x3
x3

Slide 16 - Tekstslide

GRAPHS ........
You might wonder by now:
What does the GRAPH for: 

f(    ) =                  look like? Next slide shows you the remarkable shape it has!
x3
x

Slide 17 - Tekstslide

Awesome, isn't it?

Slide 18 - Tekstslide

A good explanation about this graph is given in the Movie from the next slides!
+ This LessonUp I will share with you, so that
+ You can watch this Feelgood Movie later, 
+ Pausing whenever you like

Slide 19 - Tekstslide

Slide 20 - Video

Slide 21 - Video

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!

Slide 22 - Tekstslide

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 Homework teams assignment.

Slide 23 - Tekstslide