414 Transformation geometry (Chapter 20)
What to do:
1 On the same set of axes graph:
a y=
1
x
b y=
1
x
+2 c y=
1
x
¡ 3 d
What transformation maps y=
1
x
onto y=
1
x
+k?
2 On the same set of axes graph:
a y=
1
x
b y=
1
x+2
c y=
1
x¡ 3
d y=
1
x+4
What transformation maps y=
1
x
onto y=
1
x+k
?
You should have discovered that:
² y=f(x) maps onto y=f(x)+k under avertical translationof
¡ 0
k
¢
² y=f(x) maps onto y=f(x+k) under ahorizontal translationof
¡¡k
0
¢
² y=f(x) maps onto y=kf(x) under a stretch with invariantx-axis and scale factork.
Example 11 Self Tutor
Consider f(x)=^12 x+1. On separate sets of axes graph:
a y=f(x) and y=f(x+2) b y=f(x) and y=f(x)+2
c y=f(x) and y=2f(x) d y=f(x) and y=¡f(x)
ab
cd
O
y
x
-2
-2
11
-2
-2
-2 yx¡=¡¦()
yx¡=¡¦ ¡+¡2()
22
O
y
-2 x
+2^11
+2
+2
+2
yx¡=¡¦()
yx¡=¡¦()¡+¡2
33
O
y
x
11
-2-2
yx¡=¡¦()
yx¡=¡2¦()
22
O
y
x
11
-2-2
-1-1
yx¡=¡¦()
yx¡=¡-¦()
y=
1
x
+5
3 On the same set of axes graph:
a y=
1
x
b y=
2
x
c y=
3
x
d y=
¡ 1
x
e y=
¡ 4
x
What transformation maps y=
1
x
onto y=
k
x
?
IGCSE01
cyan magenta yellow black
(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_20\414IGCSE01_20.CDR Tuesday, 18 November 2008 10:59:24 AM PETER