Graphics Reference
In-Depth Information
s
(
x
)
s
(2
x
) and
s
(
x
)
s
(4
x
). Thegraphs of thefunctions
s
,
s
and
s
have been illustrated on [0, 2].
0.5
0.4
0.3
0.2
0.1
0.5
1
1.5
2
0.5
0.4
0.3
0.2
0.1
0.5
1
1.5
2
Noticethat thegraph of
s
is a version of
s
, scaled down by a
factor 2 in both the
x
- and
y
-directions. Scaling down by a
factor
k
turns
1
k
f
(
kx
).
y
f
(
x
) into
ky
f
(
kx
)or
y
(iii) Thegraphs of
s
s
and
s
s
s
have been illustrated
on [0, 2].
0.5
0.5
1
1.5
2
0.6
0.5
1
1.5
2
Since0
f
(
x
)
1 for all
x
, deduce that 0
s
(
x
)
, for all
x
.
.
(iv) Is
s
continuous for all
x
? See qn 6.96, the continuity of
contiguous continuous functions. Define
Givean uppr bound for
s
s
and for
s
s
s
1
2
s
(
x
)
s
(2
x
).
continuous for all
n
?
(v)
The blancmange function
Show that
s
Is
s
(
x
)
for all
x
, and deduce that the function
b
defined by
