10 Prologue
In this case, f
exprees the
relationship
or rule
betwn
a parent
and “an
ospring.
And this
relationship is
true of almost
any animal. If x
is a bird, y is a
chick.
Okay! Now
lk at this.
For example,
the relationship
betwn incomes
and expenditures
can be sn as a
function.
Like how when
the sales at a
company go up,
the employs
getbonuses?
The spd of sound
and the temperature
can also be expreed
as a function. When
the temperature goes
up by 1°C, the spd
of sound goes up by
0.6 meters/second.
And the
temperature in the
mountains goes
down by about
0.5°C each time you
go up 100 meters,
doesn’t it?
An ospring
A parent
Y
o
o
-
h
o
o!
Caviar
Sales
Down
During
Recession
X-43 Scram Jet
Reaches Mach 9.6 —
New World Record
What Is a Function? 11
Do you get it? We
are suounded by
functions.
I s what
you mean!
We have plenty
of time here to
think about these
things quietly.
The things you
think about here
may become useful
someday.
It’s a sma
oice, but I hope
you wi do your
best.
Yes...
I wi.
Whoa!
Plomp!
Ouch...
Are you a
right?
Oh, lunch is here
already? Where is my
bf bowl?
Futoshi, lunch
hasnt come
yet. This is...
Not yet? Please
wake me up when
lunch is here.
Z...
No, Futoshi,
we have a
new...
Has lunch
come?
No, not yet.
Z...
Flop
12 Prologue
What Is a Function? 13
Table 1: Characteristics of Functions
Subject Calculation Graph
Causality The frequency of a cricket’s chirp is
determined by temperature. We can
express the relationship between
y chirps per minute of a cricket at
temperature x°C approximately as
x = 27° 7 × 27 30
y g x x=
( )
= 7 30
The result is 159 chirps a minute.
When we graph these
functions, the result is
a straight line. That’s
why we call them linear
functions.
x
y
0
Changes
The speed of sound y in meters per sec-
ond (m/s) in the air at x°C is expressed as
y v x x=
( )
= +0 6 331.
At 15°C,
y v=
= × + =15 0 6 15 331. 340 m/s
At −5°C,
y v=
( )
= ×
( )
+ =5 0 6 5 331. 328 m/s
Unit
Conversion
Converting x degrees Fahrenheit (°F) into
y degrees Celsius (°C)
y f x x=
( )
=
( )
5
9
32
So now we know 50°F is equivalent to
5
9
50 32 10
( )
= °C
Computers store numbers using a binary
system (1s and 0s). A binary number with
x bits (or binary digits) has the potential
to store y numbers.
y b x
x
=
( )
= 2
(This is described in more detail on
page 131.)
The graph is an expo-
nential function.
x
y
10
1024
1
0

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