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FUNCTIONS AND GRAPHS

INTRODUCTION

We are going to study a little bit of functions. Lets begin with an example that will show you why is so important to know this topic.

The next image shows you a graph given by a tv news programme talking about the evolution of spanish unemployment in 2013.

And the second one graph shows the same information given the same day by th Ministry of Development.

 

-What do you think about the diferences between two graphs?

-Wich would be in your opinion the correct graph?

 

TRANSCRIPTION OF THE VIDEO

Now we are ready to watch a video that explain the key features of a function is, here you have the transcription:

0:00 [Voiceover] Ruby puts a dish of macaroni
0:02 and cheese into the refrigerator.
0:04 The dish was 80, 80 degrees Fahrenheit
0:10 when she put it in, and the inside
0:12 of the refrigerator was 40 degrees Fahrenheit.
0:17 The dish cooled quickly at first,
0:19 so this is gonna be interesting, quickly at first,
0:21 then slowed as it approached the temperature
0:25 inside the refrigerator, alright.
0:28 Which of the following graphs
0:30 in the mT-plane could best represent
0:34 the temperature, T, in degrees Fahrenheit,
0:37 "m" minutes after Ruby put the dish in the refrigerator?
0:42 So mT-plane sounds very fancy,
0:44 but all they're saying is is the horizontal axis,
0:47 that's our time axis, and it's gonna be measured in minutes,
0:50 "m" for minutes. And our vertical axis in this plane,
0:54 in this coordinate plane, is going to be
0:55 our temperature axis, and it's measured in Fahrenheit degrees.
1:00 So let's see what they're saying.
1:01 So the dish started at 80, at 80 degrees, at 80 degrees Fahrenheit.
1:07 So at zero minutes, right when she put it into the fridge,
1:10 it should be 80 degrees. So this one right over here,
1:13 this one is indeed at 80 degrees. This graph right over here,
1:17 this is starting at zero degrees.
1:19 Not at, it needs to start at 80 degrees
1:22 if we're gonna model what actually happened.
1:24 So this, we can rule that one out immediately.
1:27 Then when you look at these choices,
1:28 this one starting at 40 degrees.
1:31 Once again, not what we need.
1:32 We need it to start at 80 degrees at zero minutes.
1:36 So we'll rule that one out.
1:37 This one also starts at 80 degrees.
1:40 Now let's think about the shape
1:42 of what the curve should be.
1:44 They say the dish cooled quickly at first then slowed,
1:50 then slowed as it approached the temperature
1:53 inside the refrigerator. Now, does this graph describe that?
1:58 It starts, before it was in the refrigerator
2:00 it was at 80 degrees, or right when they put it in the refrigerator
2:02 it's at 80 degrees. And then it starts, its temperature declines quickly
2:07 at first, but then the rate of decline
2:10 slows as it approaches the temperature inside of the fridge,
2:14 that 40 degrees, and that seems like that this is what's happening.
2:18 The slope is become, it starts out quite negative,
2:21 but it becomes less and less and less negative
2:24 as we get closer and closer
2:25 to the 40 degrees Fahrenheit. This one over here,
2:30 after some number of minutes
2:31 we do end up at this 40 degrees Fahrenheit,
2:35 but the rate of decline is constant the entire time.
2:39 This is a line, this is describing a constant rate of decline.
2:42 But what they described is a changing rate of decline.
2:45 The dish cooled quickly at first,
2:47 so that would be a steep decline, cooled quickly at first,
2:51 then slowed as it approached the temperature
2:53 inside the refrigerator.
2:54 So the decline slows, it becomes less negative
2:57 as we approach the temperature of the refrigerator.
3:00 So you have this. . . .
3:02 this change in the rate of temperature change
3:07 and so you are going to . . . or at least I would,
3:12 pick this one right over here.
3:14 This one right over here describes a constant rate,
3:16 which is not what was described in the question.

 
ACTIVITIES

 1 In this task try to match each graph with its statement:

1. Height of a ball that bounces over time

2. Height of the water in a tank that was empty and is filling

3. Height that gets a balloon until it explodes.

4. Cost of internet usage with flat rate.

5. Height of the water in a tank that is being emptied.

6. Cost of internet use with a fixed rate of 15€ and 0.5€ per minute.

 

 2 Ask true/false this questions about the graph that describe the temperature during five days:

 

a) From 12 to 24 hours on the first day there is an increasing interval

b) We found a maximum temperature on the third day

c) From the first to the second day the temperature remains constant

d) There is a minimum on the third day

e) The maximum variation is four degrees

f) The average temperature is 37 degrees

 

 3  The following table shows the growth in cm of the head of a baby as the months pass. Try to draw the graph and write a short description of its evolution. Wich is the growth trend?. Can you say how much it will measure the perimeter at three years?

months        0     3     9     15    21    27    33

Perímeter    34    40   44    46   47     48    49

  4  Open the web linked in manipulated functions, choose two graphs and try to explain with your own words why are them wrong.

 

Well done!... now if you want to go further try to work on the links we let you in the green buttons above.

 

Short url:   https://multidict.net/cs/5253