Inverse relationships

• Wiskunde
• Middelbare school
• havo
• Leerjaar 3

Inverse relationships

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Today

• Start (5 min)
• New subject (20 min)
• Bettermarks (20 min)
• Question together  (15 min)
• Bettermarks (15 min)
• End lesson (5 min)

Exercize

Pien has got a job at the Albert Heijn and makes €8,- per uur. Give the formula with B the amount that she earns and t, the amount of hours she has worked.

Give the formula

Exercize

Pien has got a job at the Albert Heijn and makes €8,- per uur. Give the formula with B the amount that she earns and t, the amount of hours she has worked.

t	0	1	2	3	4	8
B

Inverse relationships

Pien has made some money and descides to throw a party. She buys 4 liters of wine. Give the formula for the liters wine L and the amount of persons a.

Give the formula

Inverse relationships

Pien has made some money and descides to throw a party. She buys 4 liters of wine. Give the formula for the liters wine L and the amount of persons a.

a	0	1	2	3	4	8
L

Inverse relationships

y=​x​​1​​

Inverse relationships

y=​x​​1​​

y=​x​​−8​​

Inverse relationships

y=​x​​1​​

y=​x​​−8​​

y=​x+3​​3​​

Inverse relationships

y=​x​​1​​

y=​x​​0.5​​−9

y=​x​​−8​​

y=​x+3​​3​​

Geogebra

12.3 Inverse relations

An inverse relation has got a      in the denomitor of the fraction.

For example:

The graph is called a hyperbola and has got two asymptotes

x

y=​x+3​​1​​−2

Finding asymptotes from the formula

Horizontal asymptote: 

The number that isn't in the fraction is -2

Therefore the asymptote is 

y=​x+3​​1​​−2

y=−2

Finding asymptotes from the formula

Vertical asymptote:

Set the denomitor equal to zero and solve for     :

The asymptote is 

y=​x+3​​1​​−2

x

x+3=0

x=−3

x=−3

Bettermarks

• Bettermarks 12.3
  
• 20 min
• Raise your finger if you have any questions or when you're finished
• Communicate in English please

Question together

Put your Ipad down and grab your notebook

Question 10 Bettermarks

What is the area of a garden if 5 people rent one?

The area of one garden is 9 m². How many people have rented a garden?

Solving inverse equations

Find t  if N = 23 in the formula

N=​3+t​​140​​−5

Solving inverse equations

Find t  if N = 23 in the formula

N=​3+t​​140​​−5

N=​3+t​​140​​−5

Solving inverse equations

Find t  if N = 23 in the formula

N=​3+t​​140​​−5

23=​3+t​​140​​−5

N=​3+t​​140​​−5

Solving inverse equations

Find t  if N = 23 in the formula

N=​3+t​​140​​−5

23=​3+t​​140​​−5

28=​3+t​​140​​

N=​3+t​​140​​−5

Solving inverse equations

Find t  if N = 23 in the formula

N=​3+t​​140​​−5

23=​3+t​​140​​−5

28=​3+t​​140​​

3+t=​28​​140​​

N=​3+t​​140​​−5

Solving inverse equations

Find t  if N = 23 in the formula

N=​3+t​​140​​−5

23=​3+t​​140​​−5

28=​3+t​​140​​

3+t=​28​​140​​

3+t=5

N=​3+t​​140​​−5

Solving inverse equations

Find t  if N = 23 in the formula

N=​3+t​​140​​−5

23=​3+t​​140​​−5

28=​3+t​​140​​

3+t=​28​​140​​

3+t=5

t=2

N=​3+t​​140​​−5

Solving inverse equations

Find t  if N = 23 in the formula

N=​3+t​​140​​−5

23=​3+t​​140​​−5

28=​3+t​​140​​

3+t=​28​​140​​

3+t=5

t=2

2=​3​​6​​

N=​3+t​​140​​−5

Solving inverse equations

Find t  if N = 23 in the formula

N=​3+t​​140​​−5

23=​3+t​​140​​−5

28=​3+t​​140​​

3+t=​28​​140​​

3+t=5

t=2

2=​3​​6​​

3=​2​​6​​

N=​3+t​​140​​−5

Bettermarks

• Bettermarks 12.3
  
• Until 14:40
• Raise your finger if you have any questions or when you're finished
• Communicate in English please