types of relational ships as 12.2.2 12.2.1
TRANSCRIPT
-
8/4/2019 Types of Relational Ships as 12.2.2 12.2.1
1/16
Typesof
Relationships
A S 12.2.1 ; 12.2.2
-
8/4/2019 Types of Relational Ships as 12.2.2 12.2.1
2/16
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.
-
8/4/2019 Types of Relational Ships as 12.2.2 12.2.1
3/16
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
-
8/4/2019 Types of Relational Ships as 12.2.2 12.2.1
4/16
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
-
8/4/2019 Types of Relational Ships as 12.2.2 12.2.1
5/16
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.
-
8/4/2019 Types of Relational Ships as 12.2.2 12.2.1
6/16
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
-
8/4/2019 Types of Relational Ships as 12.2.2 12.2.1
7/16
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
-
8/4/2019 Types of Relational Ships as 12.2.2 12.2.1
8/16
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 .
-
8/4/2019 Types of Relational Ships as 12.2.2 12.2.1
9/16
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
-
8/4/2019 Types of Relational Ships as 12.2.2 12.2.1
10/16
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.
-
8/4/2019 Types of Relational Ships as 12.2.2 12.2.1
11/16
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)
-
8/4/2019 Types of Relational Ships as 12.2.2 12.2.1
12/16
-
8/4/2019 Types of Relational Ships as 12.2.2 12.2.1
13/16
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
-
8/4/2019 Types of Relational Ships as 12.2.2 12.2.1
14/16
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.
-
8/4/2019 Types of Relational Ships as 12.2.2 12.2.1
15/16
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.
-
8/4/2019 Types of Relational Ships as 12.2.2 12.2.1
16/16
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.