1.1

Car A
moves at a constant speed .

1.2

At point P
car A stops and is in rest (does not move) for 1 hour, from t = 2 to t = 3.

1.3

Speed
of car A = 75 km/h.

1.4

Car B
travels at the higher speed because the gradient of the graph for car B is greater than

the gradient of the graph for car A.

distance

150 km

1.5

Average
speed of car A = ————— = ————
= 50 km/h

time

3 h

1.6

Average
speed of car B = 100 km/h.

1.7

Yes, from
t = 5 to t = 6 both cars travel 100 km in 1 hour, their speed is 100 km/h.

1.8

Yes. Both
cars travel 400 km in 6 ours. Their average speed = 66,667 km/h.

2.1

If
x = – 2, y = –1 and if x = 8, y = 19.

The points
(–2 ; –1) and (8 ; 19) are points on the line f.

We can
now say that if x = –2 then y _{ f } = –1 and if x = 8
then y _{ f } = 19.

2.2

If
y = 4 , x = 0,5 and if y = –5, x = –4.

2.3

If
x = –2, y = 19 and if x = 8, y = 14.

2.4

If
y = 13, x = 10 and if y = 17, x = 2.

2.5

P is
the point (6 ; 15)

2.6

If x = –2
then y _{ f } = 2x + 3 = –1 and y _{ g } = 18 – 0,5x = 19. Therefore, if x = –2

(a) false: 2x + 3 ≠ 18 – 0,5x because –1 ≠ 19 ;
–1 < 19

(b) true; 2x + 3 < 18 – 0,5x because –1 < 19

(c) false; 2x + 3 < 18 – 0,5x because –1 < 19

2.7

(a) false: f ≠ g because –1 ≠ 19 ; –1 < 19

(b) true; f < g because –1 < 19

(c) false; f < g because –1 < 19

2.8

(a) f < g if x < 6

(a) f = g if x = 6

(a) f > g if x > 6

2.9

MN = 20

2.10

If
x = –2 then f – g = 20 [Note: distance is ALWAYS POSITIVE].

2.11

If
x = 8 then f – g = 19 – 14 = 5 : if x = 0,5 then f – g = – 13,75

If
x = –4,5 then f – g = – 26,25

2.12

f = 0 if
x = – 1,5 ; f < 0 if x < – 1,5 ;
f > 0 if x > – 1,5

2.13

f.g < 0 if
x < – 1,5 ; f.g = 0 if x = –1,5 and f.g > 0 if
x > – 1,5

3.1

There is no
income from the sale of 0 items.

3.2

There may
be costs involved in the production process, e.g. hiring staff, buildings, machinery, etc.

3.3

A profit
is made if the income is greater than the expenses or costs.

Using the
graph we want that part of the graph where the graph of the income has a greater

y value than
the graph of the costs, we say that the graph of the income must be greater or

lie "above"
the graph of the costs. Therefore, a profit is made if f > g.

A profit is
thus made if the number of items sold is greater than the number of items at the

point of
intersection of f and g.

3.4

Income = R6

Δ y 6
3

3.5

m = ——— = ——
= —— = 1,5

Δ x 4
2

3.6

y = 1,5x

3.7

At point P f = g, i.e. the graphs have the same y value for a certain x value, i.e.
at P y _{ f } = y _{ g }

f is defined by y = 1,5x and g by y = 0,875x + 5

Therefore, at P : 1,5x = 0,875x + 5

0,625x = 5

x = 8

Put x = 8 into y = 1,5x : y = 1,5 × 8 = 12

P is the point (8 ; 12)

3.8.1

No. It
is the break even point. The income is equal to the costs. No profit is made and

and no loss is made.

3.8.2

No. A
loss is made because the income is smaller than the costs. The graph of the costs lies

"above"
the graph of the income.

3.8.3

Yes, a
profit is made because the income exceeds the costs, the graph of the income lies

"above" the graph of the costs.

3.9

Profit
from 4 items : –R2,50 (a loss of R2,50) and profit from 10 items: R1,25

3.10

12 or more items.