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