ページ1:

general mathematic
ANGEL FERRY
STEM 112
REPRESENTATIONS OF
P
RITCHIE LABAYO
LOGARITHMIC
"WEEK 8
What
I have
Learned
P.
60605
Date:
Functions
The graph of a Loganthmic funcion has a vertical
asymptote
at x=0.
"The graph of a logarithmic function f(x) = log(x) is
increasing if 6 > 1 and decreasing if 0<b<1.
6>1
The graph of the function f(x) = log b (x+c) shifted the
parent function f(x) = log b (x) to the left if c>0 and to
the right if
0
C<0.
The graph of the function f(x) = log b (x) + d shifted
the parent funcion If (x) = log b (x) upward if d > 0 and downward if d<0.
The graph of the function f(x) = a log6x strechies the parent
function f(x) = logbx if a > 1 and compresses if o<a (1.
mmico

ページ2:

l l l l l l l l l l l
Gorest Math
Tangel Jerry
Stem 112
Domain AnD RANGE
OF
Ritchie Sabayo
EXPONENTIAL
FunTions
Week 6
+.)
what I have learned p. 535
Domain of a
Function
2.
Function
3
Range of a
R
(h,+∞ x)
(-00,h)
In finding the domain and range of an exponential function,
first, for any exponential function, f(x) = ab*, the domain is
the set of all real numbers. While
the
range
is the set of
real numbers above or below the horizontal asymptote, y=d,
but does not include d, the value of the asymptote
must keep this reminder.
In studying and working at the same
time-
- In finding-
The first
master is time management, it will help
be organized. Do the
the solution, we
thing he
must
him
d
lot
to
priorities first
plan
a
time
schedule for
week
doing nothing. He
the
Can
also
to keep
him
on
time
and
not forgetting anything
set goals,
he
must
learn
to discipline
himself.
before spending your

ページ3:

REPRESENTATIONS OF
EXPONENTIAL
FUNCTIONS
0
ANGEL FERRY
STEM 112
RITCHIE
WEEK 5
LABAYO
What I Have Learned p. 508
it's
The function f(x) = 2* curves upward from.
initial value. This nature of the function has x
REAL numbers. Here the y-intercept is I
values that
(x=0). At x<0
are
the x-axis becomes
the graph. On
POSITIVE
the other hand
y
values
the ASYMPTOTE of
or f(x) contain only
infegers. Moreover, you can closerve that the constant
2 is greater than I and is not equal to zero. If this is the case
where b is greater than and not equal to 1, you will have what
we call
an exponential GROWTH. It is
an increasing function.
In the case, where 0<b<1, you will have what we call
exponential DECAY
It is a decreasing function.

ページ4:

eneral mathematics
ANGEL FERRY
STEM 112
RITCHIE LABAYO
Exponential Functions, Equations
and Inequalities.
J
WEEK 5
Additional
Activities
470
1
Exponential function
=
=
f(x)
2.)
f(x)
3.
4.
f(x) =
5
y
3(2)-71
5×
x+2
y= -5xFT
4-
3/2
-4x
Exponential equation
64+1 = 2169
x
2.
2
3.
= 14
5-36 25
Exponential inequality 6
2. 5 xH
3.
4.
5.
4
77
<30
3x+ 2
> 42
7x+1 > 73
8*>64
4. 10x = 10
2
5:5=25

ページ5:

Glenerus Muth
ANGEL FERRY
·STEM 112
WEEK 5
What I have Learned
P.445
B.
there
to
REAL-LIFE SITUATIONS
Functions
REPRESENTENG
USING EXPONENTIAL
A.) 1. Exponential function
2. y=yo (2) + A
3. half-life
4. y = yo (1/2) +/T
t
5. A = P (1+r)*
In representing exponential function in real-life situation,
to follow, it is
useful
because
it is used
are steps.
model population growth, loan interest rates, investment
etc. First
statement
we must understand
what do the
the problem, what
want to find out? Then, we must device a plan.
pattern or constructing
identifying a
P
table
can help.
Then, solve for the problem. After that
check
and
+
-answer
to besure
interpret the
c.)
If
will
of what you've done.
I will become the president of the Philippines
conduct
consent
Some
must be
programs
to
help not
to worsen
the economic state of the country, the legal age of
sexual
18 as well as marriage. We
will also conduct public meetings to inform about safe
because overpopulation is one of the
of economic problems. Spreading the
to the community will be
sex and others
main
right
cause
information
turn in being open minded and
at the
true
problems of
big
not being ignorant
the society.

ページ6:

ANGEL FERRY
STEM 112
LESSON 4:
NO.:
DATE:
GEN
MATH
RITCHIE
LABAYO
REPRESENTING REAL-LIFE
SITUATIONS
USING
Functions
WHAT
1 HAVE LEARNED
p.18
17
A relation
is
a set of ordered
element
is called
pairs
the domain while the second element
where
the first
is
the range.
2.) A function
can
be classified
as
one-to-one correspondence,
and
many- to- one
correspondence.
3.) In
a function
the independent
variable while
B.)
as
machine, the input represents.
the output is the dependent variable.
Function's significant in showing real-life striations ;
we point out and
it will
includes
in
a
and a
help us
a
use
functions
lot. Common
in real-life settings
functions in
real-life
input-output situations. For example, buying soda
the input
vending machine. You put coins which is the
soda will come out which
it will help us predict the output
For example, if
is the out put. Another one,
know
you
know
or
even
the input.
the input and function,
you
will
the output and if you know
the output and function,
you'll be able to guess the input because it's impossible to
get grape juice if you put apple as an input.

ページ7:

angel Jerry
Stem 112
General Mathematics
Ritchie Labayo
Week 3
LESSON 5: The Domain and Range of
a
Rational
Functions
Independent Assessment 229
1.) f(x) = 3
Domain: x-1=0
Range: X = -
3
y=x+3
X-1
5-1
2.) f(x) = 2x
X-4
{XER IX #4}
X =
{XER|X#1}
x4=0
xy-x=3
X = O
xy=x+3
{yER /y0}
y=2x
X=4
X-4
X = 24
4-4
xy-2y=4x
y(x-2)=4x
Xx-2
y= 4x x=2
xy-4x=2y {yεR\y±2}
3.) f(x) = x+3
4.) f(x)
5x-5
= 2+x
2x
5₁) f(x) = (x²+4x+3)
x²-9
5X - 5 = 0
5x = 5
y=x+3
5x-5
y
=
5x+3
5
X = y+3
x = 1
54-5
5x-|
5xy-5x=y+3
57-4-0
5x-1
{XER 1x+1} 5xy-y=5x+3
2x=0
X = O
y (5x-1)=5x+3
y=2+x
{XERIX #0}
x²-9=0
2
x = ±3
de
5
x=15
{YER\y # } }
2xy-y=2
2X
x=2ty
2y
y(2x-1)=22x=
y = 2 x=1 x = 2 1/2
2x-1
2xy = 2+y 2x-1= 0 {YER\y* 1/2
x = (y²+4y+3)
y29
20x = (y+1) (y+3) xy-3x = 4+1
{XER 1x ±3}
4+35-3)
xy-y=3x+1
x= y+1
y(x-1)=3x+1
f f B
y-3
y=3x+1
Range: y = (x²+4x+3)
x29
X-T
x-1=0
X = 1
✓ VICTORY
{yER ly#1}

ページ8:

ANGEL FERRY
STEM
112
LESSON
4: SOLVING
REAL-LIFE
PROBLEMS
INVOLVING
FUNCTIONS
NO.:
DATE:
GEN MATH
RITCHIE LABAYO
WHAT
1 HAVE LEARNED
P. 104
In
solving problems involving
functions, first, I always
identify what the problem.
addition, division
or
is looking for, if it's substraction,
multiplication. Then, i make a plan or
the appropriate formula.
what you called finding
- problem. Because if you use
answer.
careful with
_also
to
a wrong
_and
becoming
Then
after
1
came
up
with
to the
wrong formula, obviously, you'll end up
After that
1
+
1.
begin solving it
the signs, substituting, transposing etc.
it. i always checking if the
become
an answer. I look back or check
other way around, the answer
the raw given and the given must be the answer.