Everything Maths Grade 10

On the same set of axes, plot the following graphs (b= 2,a= 1andqchanges):

1.y 5 = 2x 2

2.y 6 = 2x 1

3.y 7 = 2x

4.y 8 = 2x+ 1

5.y 9 = 2x+ 2

2 1 0 1 2

y 5 = 2x 2

y 6 = 2x 1

y 7 = 2x

y 8 = 2x+ 1

y 9 = 2x+ 2

Use your results to deduce the effect ofq.

On the same set of axes, plot the following graphs (b= 2,q= 0andachanges).

1.y 10 = 1 2 x

2.y 11 = 2 2 x

3.y 12 = 1  2 x

4.y 13 = 2  2 x

2 1 0 1 2

y 10 = 1 2 x

y 11 = 2 2 x

y 12 = 1  2 x

y 13 = 2  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 is shifted vertically upwards byqunits.


• Forq < 0 , the graph is shifted vertically downwards byqunits.

The horizontal asymptote is shifted byqunits and is the liney=q.

The effect ofa

The sign ofadetermines whether the graph curves upwards or downwards.

For 0 < b < 1 :

• Fora > 0 , the graph curves downwards. It reflects the graph about the horizontal asymptote.


• Fora < 0 , the graph curves upwards.

Forb > 1 :

• Fora > 0 , the graph curves upwards.


• Fora < 0 , the graph curves downwards. It reflects the graph about the horizontal asymptote.
  b > 1 a < 0 a > 0

q > 0

q < 0

Table 6.4:The effect ofaandqon an exponential graph whenb> 1.

180 6.5. Exponential functions