function and their properties

7/30/2019 Function and their Properties

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CARMEN MONZIES AMPARO SANZ2009/2010


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1. An electrician charges 30 for each job and 25 per hour. Find a formula for the

electricians charge in euro, and use your formula to determine the charge of a job thattakes 3 hours. ( ) 25 30

(3) 25 3 30 105

f x x

f

2. Theatre tickets cost 15.50 for adults and 7.80 for children. Four adults took a

group of children to the theatre. The tickets cost 101 in total. How many childrenwent to the theatre? Write the formula that gives the total amount for 4 adults varying

the number of children (x). Solve the problem with an equation.4 15.50 7.80 101

5

x

x

( ) 7.80 62f x x

3. The high speed train travels at 230 Km/h. What is the function that describes the

distance (in km) depending on time?( ) 230f x x


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4. This graph shows Bens height from 2 to 18 years of age:

a. What are the variables involved?

Age and height.

b. What scale is used in each variable?

Ten units in y-axis, and one unit in

x-axis.

c. How many centimetres did he grow

from 5 to 8 years of age? 20 cm.

And from 15 to 18? 10 cm

In which of these time intervals was

the growth greater? In the firstd. Notice that the end of the graph

shows a slower increase. Do you think

his height will increase a lot more or

stabilise around a specific value? It will

stabilise around 180 cm


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5. To measure lung respiratory capacity a test is done that consists of inhaling to the

maximum, and then exhaling as fast as possible into a device called a spirometer. This

curve indicates the volume of air that goes into and out of the lungs.

a. What is the volume at first? 1.5 l

b. How long did the observation

take? 18 seconds

c. What is the maximum capacityof this persons lung? 4 l

d. What is the volume 10 seconds

after the test started? 1 l

And at the end? 0.5 l


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6. This graph shows the number of car accidents in recent years in a given town

a. What year was the number of car accidents highest? 2000 How many accidentswere there? 385b. What year was the number of car accidents lowest? 2006 How many accidents

were there? 244c. Study the increase and the decrease in the number of accidents over the years

indicated in the graph above. The number of accidents decreased in [2000, 2002] and[2003, 2006]. They increased in [2002,2003]


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7. Four friends, Martina, Tanner, Ben and Kate meet at the door of the auditorium to go to a

concert of their favourite music band. When they meet, they talk about their journey to the

auditorium:MARTINA: I came by car. Besides, I was lucky because I didnt get caught in any traffic jams and

I came directly.TANNER: I was on my way when I realised that I had forgotten my ticket. I had to go back to getit and then I got here with no problems.BEN: I was walking fast until I met Ann on the way, then we came together walking more slowly.KATE: I came by motorbike and I came directly using a shortcut. I didnt come as fast as Martina,

but I didnt stop on the way.Each of these graphs shows the way they travelled from their homes to the auditorium:Which graph corresponds to each person?Who lives closest to the auditorium?Whose journey took less time?

A: Ben; B: Martina; C: Kate; D: TannerTanner, whose graph is D, lives closest to the auditorium.

The journey that took less time was B


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8. The carriages in a big wheel go up and down as the wheel goes round. This graph

shows the function time-distance from the floor of one of the carriages:

a. How long does it take for the wheel to make a complete turn? 40 secondsb. Observe the maximum height of the wheel and indicate the radius of the wheel? The

maximum height is 16 m, and the radius of the wheel is 8 m long.c. Explain how to calculate the height after 130 seconds without using the graph. As this

is a periodic function and 130 = 40 x 3 + 10, f(130) = f(10) = 8, the height of the wheelwill be 8 m.


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9. An experiment has been done with two species of living beings. The graph shows the

growth of each of them, which have grown separately and in exactly the same

conditions

a. Does the number of individuals in each species grow indefinitely or stabilize around a value? It

stabilises around a valueb. What value, in thousands, is the tendency for species A (under the conditions studied) which

are shown in the graph? 800 individuals per ml

c. Which species multiplies quicker? Species A


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d. Observe in the following graph what happens when both species grow

in the same cubicle, competing for food:

e. Both populations grow more slowly when they are together than when they are separate. What

value does the number of individuals in species A approach in this case? 200 individuals per mlf. What is the maximum number of individuals in species B? 110 individualsg. What value does the number of individuals of this population tend towards as the days go by?(As the population in species A multiplies faster, it consumes more food; therefore population inspecies B tends to disappear) The number of individuals of B tend to 0.


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10. Lewis took 2 hours to travel from his house to a city 200 km away where he had a

business meeting. He was there for 2 hours and took 4 hours to come back home.a. Draw the graph time-distance to his house.

b. If he maintains a constant velocity on his journey to the city, what is the velocity?

The velocity is v = distance/ time = 200 / 2 = 100 km/hc. If he also maintains a constant velocity on his journey back from the city, what is thevelocity? V = 200 / 4 = 50 km/h


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11. A merry-go-round accelerates for 2 minutes to reach a velocity of 10 km/h. The

velocity remains constant for 7 minutes and in 1 minute it decreases to a stop. After 5

minutes stopped, it starts another round. Draw the graph time-velocity.


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12. In a gym you must pay 10 for enrolment and 30 each month.a. Rose has been going to this gym for 5 months. How much money has she paid

total? 10 + 30 5 = 160

b. How much has Albert, who has been going for 2 years, paid? 10 + 30 24 = 730

c. Draw the graph of the money paid in total according to the number of months you go

to the gym.


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x (pounds) 0.5 1 1.5 2 3 4 xy (kg) 0.225 0.45 0.675 0.90 1.35 1.80 0.45x

13. A pound weighs 0.45 kg. Complete the following table:a. Represent the function of converting pounds into kilos.b. Work out the analytical expression that relates both variables.


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TIMETABLE: 9.00 am to 9.00 pmThe first 2 hours..............................................................freeThe third hour or following fractions................................. 1

14. The town hall of a village wants to promote the use of bicycles. So, they decided to

hire out bikes according to the following fares:The maximum time is 12 hours a day (from 9 am to 9pm).Represent the function time of bike use-costin the form of a graph.


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15. The dose of a medicine is 0,25 g per kilo the patient weighs, up to a maximum of 15

g.a. How many grams does a boy who weighs 10 kg. take? 0.2510 = 2.5 gb. How much do you have to weigh to take the maximum dose? 15 : 0.25 = 60 kgc. Represent the functionpatient's weight-indicated dose? y = 0.25x

function and their properties

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