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Typesof

Relationships

A S 12.2.1 ; 12.2.2

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In maths, functional relationalshipshave the form y = f(x). The variable y

is dependent on x, which is theindependent variable.

y = 3x2 is regarded as a rule thatdefines the relationship between xand y.

If x = 2 then y = 12 and (2 ; 12) isthe ordered pair in a Cartesian

plane.

We must be able todescribe, display andcompare real-life situationsusing words, tables,equations and graphs.

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Price (R)

in 2005

Price (R)

in 2006

50

100

150

200

250

106

159212

265

The average inflation rate for2005

is 6% per year.Complete the table:

Represent thedata graphically.

53

Price in 2005

0 50 100 150 200 250

300

250

200

150

100

50

0

Pric

ein2006

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Price in 20050 50 100 150 200 25

300

250

200

150

100

50

0Pr

ice

in200

6

If the price of an objectin 2005 is R120,

determine the price in2006.

If the price of an object

in 2006 is R210,determine the price in2005.

R127

R198

If the inflation rate was 10%, describe theshape of the new graph.

Similar, but from

origin steeper thanold ra h

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This graph compares the costs ofrenting

copy machines from two suppliers.

No of copies in thousands

0 2 4 6 8 10 1

500

400

300

200

100

0Cost

pe

rmonth

Whatinformation isgiven by the

intersection ofthe two lines?

A

BCost and no.of copies for

both are thesame.

When would you rent from supplier A?

copies are less the 8000 per month.

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A car valued at R100 000 waspurchased

on 1 April 1994. The book value at theendof the next 12 years is shown below.

year Bookvalue (R)

0 100000

3 72900

6 53100

9 38700

12 28200

Represent thisdatagraphically.

0 3 6 9 12year

Bo

okvalu

ein

R(100

0s)

100

80

60

40

20

0Which is theindependent variable?

year

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Estimate the book value of the car after 8years?

0 3 6 9 12year

Book

valuein

R(100

0s

)

100

80

60

40

20

0

If the depreciation was 10% p.a., write anequation to illustrate this situation.

A = 100000(1+10%)n

= 100000(1,1)n

Could the bookvalue of this car be

zero? no

After how manyyears is the car only

worth R60 000 ? 4,8 years

R43000

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t 0 6 12 18 24 30 36B

The relationship between time(t) in hours and the no. of TB

bacteria (B) growing underunrestricted conditions is givenby B = 5 x (2)t/6Complete the table

205 10 8040 160 320

What do you notice about therelationship between B and t ?No. of bacteria (B)

doubles every 6hours.

Represent this datara hicall .

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t 0 6 12 18 24 30 36

B 205 10 8040 160320

0 6 12 18 24 30 3

t in hours

350

300

250

200

150

100

50

0

Bacteria

no.

At this rate thebacteria wouldcover the earth inno time. Why does

this not happen?

Estimate theno. of

bacteriapresent after21 hours.56 hours

growing conditionsnot always very

good many die

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Linear inequalitiesLinear inequalitiesAn inequality uses a greater than (>) or

greater than or equal to () sign, less than( 2 or 4 < 1 or x 5 etc.

If y > 7 then possible solutions are y = 8; 9; etc.If t 4 then possible solutions are t = 4; 3; 2 etc.

How to remember the inequalitysign:The open side of the sign always

has the larger quantity.

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Which of the following orderedpairs are solutions to 3x + 5y

6 ?3(2) + 5(5) 16

31 16

3(0) + 5(1) 165 16

3(4) + 5(1) 16

17 16

True

False

True

3(2) + 5(2) 1616 16

True(2;2)

(4;1)

(2;5)

(0;1)

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2x + 3y < 62.

If x = 0 then y = 2If y = 0 then x = 3

Intercept method

x

y

Pick any point

on one side ofthe graph.

Does this point

satisfythe inequality?

Try (0;0)

2(0) + 3(0) < 60 < 6

So, shade thearea with the

point.Ye

boundaryline

The line is dotted as the pointson the boundary line are not

solutions.

-2 -1 1 2 3

3

2

1

-1

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Time in hours (t)0 1 2 3 4 5 6

250

200

150

10050

0

This graph is used to locate safe andunsafe speed zones, in town, for d =60t.

Indicate thesafe speed

zone.

Dista

nceinKm

(d

)

d 60t

The point (3;180)

lieson the graph.What does 180

mean?Travelled 180 km in 3 h.

At what speed is a cartravelling to satisfy

(3;275).

Is this speed safe?

Speed = 275 /3

91,7 km/h

No

3.

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yx > 1 (1)x + 3y 3 (2)

Graph these inequalities on the same axes.

More than oneMore than one

The arrow shows theregion where the

inequality is true.

Show theoverlappingarea.Which inequality

is true for (1;2) ?Graph (2)

x-2 -1 1 2 34

0

3

2

1

-1

Does (3;0) fall within the overlappingarea?

Yes

1.

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Sketch the inequalities below on thesame set of axes when x 0 and y0.

y 4 (1)y x + 1 (2)3x + 4y > 12 (3)

0 1 2 3 4 5

5

4

3

2

1

0

Show theoverlapping

area.Give three points within this region.

Any three: (1;3) (1;4) (0;4) (2;3) (3;3) (2;4) (3;3)

x

y

2.