1TH/Vwo §6.5 Comparing graphs

• Wiskunde
• Middelbare school
• havo, vwo
• Leerjaar 1

§6.5 Comparing graphs

Good morning!

Good morning, everybody!

Let's go through an exercise!

exercise 

This graph shows you

 the cost when

 hiring a lawn mower

(=grasmaaier).

exercise 

Because 2 graphs are drawn in 1

coordinate system,

we can COMPARE them!

exercise

Task 1:

After how many days is the price 

you pay at Praxis 

the same as at Finefix?

Key in in next slide.

Task 1:
After how many days is the price
you pay at Praxis
the same as at Finefix?
Key in your answer.

exercise

Task 1:

So for 4 days the prices are equal. Both

companies then charge 50 euros.

We call the point (4, 50)

the Point of Intersection (= snijpunt)!

exercise 

Task 2:

If you hire a lawn mower

 for 2 days, which company is 

 cheapest?

Answer in next slide.

For 2 days ....

1. better choose for Praxis
2. it depends
3. better choose for Finefix
4. doesn't matter

Explanation exercise ,

Task 2:

If you hire a lawn mower for 2 days, what is 

the cheapest?

1. Go to '2 days' on the horizontal axis.

2. Go up and see which graph is highest.

3. Well, Finefix' graph lies lower,

4. so Finefix is cheapest for 2 days!

exercise 

Task 3:

If you hire a lawn mower for 5 days,

which company is cheapest then?

Key in in next slide.

For 5 days ...

1. Praxis is cheapest.
2. Doesn't matter.
3. Finefix is cheapest.
4. idk

Explanation exercise 32,

Task 3:

If you hire a lawn mower for 5 days,

which company, which is cheapest?

Go to 5 days on the horizontal axis.

Go up and see which graph lies lowest.

Praxis' graph is lowest for 5 days,

so then the price is lowest too! 

exercise 

Task 4:

Which graph has a fixed amount?

(That is the amount you have to pay, 

no matter how many days they will work

for you!)

A fixed amount ...

1. Graph for Praxis has one.
2. No clue at all.
3. Graph for Finefix has one.
4. Both graphs have one.

Explanation exercise ,

Task 4:

Which graph has a fixed amount?

The graph for Praxis starts at 10 euros.

That's what you have to pay before you have used 

this carpet cleaner for even one minute!

That's why we call this a FIXED AMOUNT.

The amount is fixed, no matter how long you use it. 

Question: What to do first, when making this task ?

ANS

First you have to ....

Solution:

Make a TABLE, indeed!

In exercises 33a. and  34a  they ask you to make a graph from a formula.

Also for those tasks MAKE a TABLE first!

How else do you know which points lie on the graph?!

However, a TIP for this follows now.

This is how the

 SOLUTIONSBOOK does it.

However, why including so may points in the TABLE?

They all lie on the same straight line!

So 3 or 4 points will be enough. For example number 0, 10 and 16.

The two graphs have a point

of intersection.

I read off:   (5, 3.5) is the p.o.i.

However, it is NOT a grid point, so I cannot be sure.

Fortunately I can also CALCULATE the coordinates!      

If you have no clue what is meant here,

watch the following slides! You will see:

- two graphs that have a point of intersection

   that you can READ OFF

- after this the FIRST COORDINATE will be FILLED in in

   both FORMULAS, to see if we get THE SAME ANSWER!

In this lessonup you have learned .....

I'd much better ASK YOU, what you've learned!

Think of a 'general description' (=algemene beschrijving) for what you learned.

I have learnt ...

Homework time

Make §6.5. You may skip 30.

- correct with Solutionsbook