Functions and their graphs Real-life graphs · PDF fileFunctions and their graphs Real-life graphs Colegio Herma. ... Beaker A How would the graphs for beakers B and C compare to this?
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Functions and their
graphs
Real-life graphs
Colegio Herma. Maths Bilingual Departament Isabel Martos Martínez. 2015
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Plotting graphs – using a table of values
When we plot a graph we usually start with a table of values.
The values in the table usually come from a formula or
equation or from an observation or experiment.
For example, a car hire company charges £30 to hire a car
and then £25 for each day that the car is hired.
This would give us the following table of values:
The cost of the car hire depends on the number of days. The
number of days must therefore go in the top row.
Number of days, d
Cost in £, c
1 2 3 4 5
55 80 105 130 155
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Plotting graphs – plotting the points
Use the table of values to plot the points on the graph.
Number of days, d
Cost in £, c
1 2 3 4 5
55 80 105 130 155
0
0
30
40
50
60
70
80
90
100
110
120
130
140
150
1 2 3 4 5
Number of days
Cost
(£)
It is most accurate to use a small
cross for each point.
If appropriate, join the points
together using a ruler.
Lastly, don’t forget to give the
graph a title.
Cost of car hire
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Science experiment
Mass of object moving down
ramp (grams)
Time taken for object to move
down ramp (seconds)
100
4
150
7
200
12
250
17
Mass of object (grams)
0
4
8
12
16
20
0 50 100 150 200 250 300
Tim
e t
aken
(seco
nd
s)
We can join the points
using straight lines.
Do the intermediate
points have any practical
significance?
How could we make the
graph more accurate?
Interpreting graphs
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Filling flasks 1
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* Filling flasks 2
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Interpreting the shapes of graphs
150
0
50
100
10 20 30 40 50 60 70 0 80 90 100
Eating a bar of chocolate
Ma
ss o
f ch
oco
late
(g
)
Time (seconds)
Jessica eats a bar of chocolate. This graph shows how the
mass of the chocolate bar changes as it is eaten.
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Interpreting the shapes of graphs
This graphs shows how the temperature of the water in a pan
changes when frozen peas are added.
Time
Te
mp
era
ture
of w
ate
r
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Which graph is correct?
In an experiment a group of pupils poured water onto a
sponge and weighed it at regular intervals.
Each time the sponge soaked up all the water.
Which graph is most likely to show their results?
Ma
ss o
f sp
on
ge
(g
)
Volume of water (cm3)
Mass o
f sponge (
g)
Volume of water (cm3)
Mass o
f sponge (
g)
Volume of water (cm3)
Graph A Graph B Graph C Graph D
Mass o
f sponge (
g)
Volume of water (cm3)
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Sketching graphs
A group of pupils are conducting an experiment. They fill three
beakers with boiling water and record the temperature of the
water over time.
Beaker A has no wrapping, Beaker B is wrapped in ice and
Beaker C is wrapped in insulation fibre.
The temperature graph for
beaker A looks as follows:
Time (minutes)
Tem
pera
ture
(oC
)
Beaker A
How would the graphs for
beakers B and C compare
to this?
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Sketching graphs
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Matching graphs to statements
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