Fungsi Eksponen Matematika Peminatan Kelas X - Apersepsi Masalah COVID-19

Hi, assalamualaikum warahmatullahi

wabarakatuh, meet me again with Deni

Handayani on the Metland channel in

this video we will learn about

exponential functions What is the exponential function like

and how is the graph of

this material is quite important for us to learn

because it is widely applied in

real life such as flower problems,

bacterial and viral breeding problems

such as the moofeat 19 virus which is currently

infecting our country, many

are reporting that coffee 19 is

growing exponentially like the

following news

[Music]

Hi and this is a graph of the growth of

copy 19 in Indonesia, well in

this video we will learn What is

the graph of the exponential function Okay,

let's go straight to the material closed

[Music]

Hi, okay, now we will learn the

exponential function, we start from the

general form first, this is the general form of the

exponential function FX = kakal power x x

is called a free variable or

variable so X can be any number as long as the

condition X is a real number member

okay, Sis, this is a constant and

A is called a base or

base number, well there are conditions Friends, the

first one cannot be negative, meaning

Dad must be more than zero and the second one is

only not worth one okay so

if we make a number line

Hi for the value of a b this is a number line

yes first it must be more than zero

for example the number here is more than the

number from the right novel yes No from

zero to the right well it turns out that the water

cannot be worth 11 it is on

the right 01 is here so only

that can not be here so this is

broken here friends can

The Key he stock broken here

so this is the possible value of a

Hi the possible base value between zero

and one and from one to the right or

greater than one so we divide the

two intervals here

where zero is less than a less than 1

then the interval to the right of one is

only more than one later we will

discuss how it affects

the graph when it is only between 1

and 0 or when A is more than one

yes and how does the value of Kak

itself affect the constant how when

the constant is negative and how

when the brother is positive how does it

affect the graph of the

exponential function. well for FX FX or

friends can change it to y y = *

Alfamart exigua this problem is called

a dependent variable so its value

follows the domain value that follows the

x value when the accent changes then it

also changes Okay Now

let's learn about the exponential function graph

Hi Okay to show the graph

here I use the

geogebra application when preparing a

function fx = k times the power of x we

follow the general form of the

exponential function and the value of k and the value of A we just

make a slider so we can immediately

see how it changes to

the graph later

Hi Okay let's try Oh yes pay attention

here when there is only one that's

why the condition can't be only one

when there is one the graph is a

linear graph straight graph yes This is not an

exponential function Now we

slide when there is only more than one

friends look at the graph it looks like

this

Oh yes it becomes a monotonically

increasing graph friends meaning monotonically increasing

when X The bigger the more to the right

then the graph he is getting up

like this this is a monotonically increasing graph

when aanya yes more than one if

we slide yes if we slide the

bigger only he will get higher

Hi When the bigger only he

gets higher

hi okay Well now what if

we just change it to eh between zero and one

more than zero less than Let

's shift it like this here

only that 0.6 pay attention to the graph it is

monotonically decreasing yes the graph is monotonically decreasing

when the aanya is less than 1 more than

zero Well that's necessary friends note so the

Aa it affects the graph

will be monotonically increasing or watching

down when only more than one

monotonically increasing when only less than 1

more than zero it is monotonically decreasing

now how does this value affect Sis

but the older sibling is positive then the

exponential function is above the X axis Men

he is above the x axis now if

we change it seems to be negative

Hi automatically the graph becomes

Inverted yes Well when the older sibling is negative

this graph seems to be mirrored yes

as if mirrored so the function will be

reversed when Anya is less than 1 it

becomes monotonically increasing when the older sibling is

negative and vice versa when Anya is more

than one it becomes monotonically decreasing further

down when the constant is negative

hi okay hi okay

here there is something called an

asymptote yes asymptote grab the line that is

getting closer to the exponential function well

in the standard one week the function

like this y = k Kaliabang card X then

the asymptote is the x-axis itself

friends pay attention to this x-axis it is

getting closer to the exponential function but

actually it never intersects yes

Even though it looks like it intersects this

never intersects Hi

this never intersects well the

x-axis or y = 0 this is the asymptote

for a standard function like this

Well if we add the function we

add for example

Hi to Sis you power x

plus 2 for example

Let's see the effect well the graph

it will rise as far as two units up

so if we add how much for example

friends add 5 then the

standard graph it will rise up as far as

five if we reduce it then it will go down well

this will change the asymptote yes if

Sis you ^ x + 2 then the asymptote will

be Y = 2 fish place here I

write y =

hi okay

Let's see y very when the function

is ye Sis Kaliabang kates add2

we see it turns out Y = 2 he becomes

the asymptote eh so the asymptote let's

just look at him plus how many Sis additional

power x plus n for example then NY = n

that is the asymptote Okay clearly yes this

is an exponential function if we

look at this graph it resembles the

growth graph of coffee 19 that

I showed earlier Now we discuss

questions related to exponential functions

hi hi Hi Okay

Dear let's discuss the first example

known function graph fx = 3 times two to the power of

one min x the graph

passes through the point neh this is the choice the

answer choice is the abscissa is the same yes X Y

= 2 all so we just enter we

replace XL with two we look for F2

friends three times two to the power of one

min exe we replace it with two so

three times 2 ^ 1 minus two yes negative

13 times two to the power of negative 1 is the

same as 1/2 right eh three times 1/2

the answer is 3/2 so when xy2

is 3/2 then the coordinate point

is 2,3 or two is there any so the

answer is B Okay a let's

discuss question number 2 function graph fx =

Hi Sis times 2 ^ 2x min 3 passes through the point

two comma negative 8 negative value 5 ke

is well here we just substitute

first yes x and y values ​​So these two

as X and negative 8 this yee we

enter here yes we substitute later

we look for the value it seems well this effect

may friends change to y so

this function equation we change to

y = Sis times 2 ^ 2X minus three we

replace Y with negative 8 negative 8 =

k times two to the power of two XE we change

to

Hai minus three earlier negative 8 = k

times two to the power of two times 244 minus

three right 1 yes 2 really this one is clear

okay so it seems how many legs =

negative lakman divided by two

Hai divided by two or it seems to be

negative 4 what we are looking for is negative

5k negatively then that means negative five

times how much is negative Question 4

Oh yes negative five times negative 4

positive 20 friends far away so

the answer is eh 20 okay very we

discuss question number 3 the graph of the function fx =

half the power of x is shown in

the picture yes FX = after half the power of

x well here only that's half remember

earlier when it's only less than one then

the graph will be monotonically going down friends

yes will watch down so the answer is

between UB customs which eh this monotonically goes up

the further to the right the higher this is

impossible yange also this monotonically

goes up this is also impossible Well we

just choose between a & b or D the way

we just look for the point of intersection with the

Y axis eh

Hi the function FX = half the power of x

how to find the point of intersection with the y axis

friends enter x = 0 replace XL

with zero so we will look for f0 f0

how much does it mean half the power of zero

whatever the number is other than zero

if we ^ know how much then only

one means it will cut the y axis

at equal to one we see the option

A this cuts the y axis at four

options B cuts the y axis at 2 and

option D this cuts the y axis at

one so the answer is D Okay together

we discuss the fourth example

Hi the graph FX = negative 2 times 3 ^ x

is shown by well here look at the value

it seems like it is negative two

remember earlier when the older sibling is negative then

the graph of the exponential function is below the

x axis friends so it's impossible

the answer to this one is not maybe

then it's impossible that this one is

there and the one D here is the graph above the

x-axis so it's impossible that the answer is that

well our choice is just a spot

look for the intersection point friends the

intersection point and

Hi the method is the same as the previous question

we just replace XL with zero yes there

the effect is the same as negative 2 times 3 ^ x

we ​​replace the fb with 0xc with zero

means negative two times three to the power of 03

^ No that's one in negative two times one

is negative 2 so it cuts the y-axis

at the point y = negative 2 we see the choice

that c is correct yes negative 2 and the one oh yes the one that

c is correct which eh is also correct

Hi Well if this B is wrong why

Because He cuts at negative 3 this is

wrong so our choice now is between

c or e well the difference is this c

graph is an increasing function if the one eh his

graph is monotonically decreasing where is the answer

well the method Just try it like this

Hi here ask negative friends

we just take the one that is not positive

first the one to positive for example FX =

positive two times 3 ^ x here only

3 if three he is monotonous up or not

well the graph will be like this

if it seems positive if it

seems negative like it is mirrored it

will go down friends it will be like this well

this is when it seems negative two so the

answer is definitely which one goes down which

one eeg so the answer is f

okay let's discuss question number 5 the

following statements

are related to the function graph fx = 3 to

the power of 2 min x minus 4na

which statement is correct we will look for the

correct statement the

first statement the function graph fx is monotonically

increasing well here friends have to be

careful here only positive Yes only

posts it is

possible friends will

conclude that it is monotonically increasing but

pay attention to the Excel value friends

the power so if we describe

using the properties of this exponent we can

write it as FX = 3 to the power of two times

three to the power of negative X can right

then minus 4/5 with nine

times three to the power of negative x minus 46 to

the power of SY is negative so

if we enter the action one then it

will be three to the power of negative one

if x is one then here it is 3 to the

power of negative 1/1 third when

the action is Two we enter here this

will be three to the power of negative 21

hiding Well from here we see

Oh it turns out that when we enter x

the greater the value this will be

smaller friends

yes it will be smaller because the exponent is

negative then the graph will definitely

be a graph that goes down yes it will go

down because the exponent is negative

so the answer is the statement monotonically

increasing this is wrong monotonically decreasing this is only

correct Okay the graph is a graph that is

monotonically decreasing The reason is because

the exponent is negative the

third statement the graph of the fx function cuts the y-axis

at point 0.9 yes we try to replace the

action with

Oh that means this will be nine

times 3 to the power of 0340 right one minus 4G

in Here here we get 9

minus 45 So the point of intersection is

0.5 this third statement is wrong the

fourth statement the graph of the fx function

cuts the as has a flat asymptote Y =

4 the asymptote just look at it is added

or subtracted this is minus four which

means the graph will go down the

standard graph will go down as far as four

units down Yes so the asymptote is the

correct one is y = negative 4 so

this statement is wrong

Hi the fifth for X The greater

the value of FX approaches negative 4 Well this is

correct, it means the asymptote is y =

negative 4 so the correct statement

is the second and fifth statements are there

2 and 5 The answer is d Okay, a person,

let's discuss question number 6, the flat asymptote

of the function graph fx = 3 times six to the

power of x plus 4, which asymptote

Well, friends, don't immediately

take Y = 4, yes, we have to multiply Ken

FX = 3, we you with this becomes

three times six ^ X3, we multiply the four

Bati plus 12 Well, so the function is

like this, friends, so from here, the

asymptote is seen,

this is Y = 12, the answer is e Okay, let

's discuss question number 7

in the result area of ​​the function fx = 2 to the power of 3

x minus 4 plus five is the

result area, that means the value is the

value Well, let's see first, this

graph is monotonically increasing or watching

down, the aanya is positive and the action is also

positive, then the

graph must be monotonically increasing, the graph

will be like this Well, here the

asymptote here is flash 5 means

the asymptote is y = 5 the asymptote is the one over

here first

Hi the one over here is y =

Hi Yeh okay

Hi this is the x-axis this is the y-axis

means the value is impossible it

cuts the axis it is impossible to cut y = 5

yes the graph is impossible to cut y =

5 so automatically the graph is it

will continue here meaning above Y = 5

meaning the result area is y is more

than five above Y = 5 means J is more

than five it is more than five And Y is a

member of real numbers the answer is

C Okay those are examples of questions and

discussions of exponential function problems

or exponential functions See you in the

next video Assalamualaikum

warohmatullohi wabarokatuh