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 > 0q > 0q= 0q < 0Table 6.3:The effects ofaandqon a hyperbola.170 6.4. Hyperbolic functions