The Manga Guide to Calculus

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

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