10 Prologue
In this case, f
exprees the
relationship
or rule
betwn
“a parent”
and “an
ospring.”
And this
relationship is
true of almost
any animal. If x
is a bird, y is a
chick.
Okay! Now
lk at this.
For example,
the relationship
betwn incomes
and expenditures
can be sn as a
function.
Like how when
the sales at a
company go up,
the employs
getbonuses?
The spd of sound
and the temperature
can also be expreed
as a function. When
the temperature goes
up by 1°C, the spd
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 ospring
A parent
Y
o
o

h
o
o!
Caviar
Sales
Down
During
Recession
X43 Scram Jet
Reaches Mach 9.6 —
New World Record
What Is a Function? 11
Do you get it? We
are suounded 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
oice, 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
bf bowl?
Futoshi, lunch
hasn’t 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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