Everything Maths Grade 10

3.y 3 =

1

x

4.y 4 =

1

x

+ 1

5.y 5 =

1

x

+ 2

Use your results to deduce the effect ofq.

On the same set of axes, plot the following graphs:

1.y 6 =

2

x

2.y 7 =

1

x

3.y 8 =

1

x

4.y 9 =

2

x

Use your results to deduce the effect ofa.

The effect ofq

The effect ofqis called a vertical shift because all points are moved the same distance in the same direction
(it slides the entire graph up or down).

• Forq > 0 , the graph off(x)is shifted vertically upwards byqunits.


• Forq < 0 , the graph off(x)is shifted vertically downwards byqunits.

The horizontal asymptote is the liney=qand the vertical asymptote is always they-axis, the linex= 0.

The effect ofa

The sign ofadetermines the shape of the graph.

• Ifa > 0 , the graph off(x)lies in the first and third quadrants.

Fora > 1 , the graph off(x)will be further away from the axes thany=

1

x

.

For 0 < a < 1 , asatends to 0, the graph moves closer to the axes thany=

1

x

.

• Ifa < 0 , the graph off(x)lies in the second and fourth quadrants.

Fora < 1 , the graph off(x)will be further away from the axes thany=

1

x

.

For 1 < a < 0 , asatends to 0, the graph moves closer to the axes thany=

1

x

.

a < 0 a > 0

q > 0

q= 0

q < 0

Table 6.3:The effects ofaandqon a hyperbola.

170 6.4. Hyperbolic functions