Vertical Stretch Help

[spice ivy]

Could anyone please help me with these problems? I keep on getting confused

[austere condor]

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[spice ivy]

these truely don't make sense can anyone help please

[past panther]

inversion of a polynomial is not going to be a logarithm

and you can watch the transformation of (0,0) to decide which of the last 2 it is

though really it's good to know how to transform

vertically compressed just means divide

x^3/7

[spice ivy]

so you basically just cancel out your options?

it'd be the first for that one then right

[past panther]

shifted left means you change x to (x+5)

[spice ivy]

oh wait no

d?

[spice ivy]

but like when we inverse across y and shift to the right it becomes so complicated

[past panther]

(x+5)^3/7
inverted means
7x = (y+5)^3
y + 5 = cbrt(7x)
y = cbrt(7x) - 5
then down 6 you get cbrt(7x) - 11

[spice ivy]

its -x

and then -x + 3 soemhow

[past panther]

wha

just do them one at a time

[spice ivy]

oh so second to last

thats fair

what would make it a log answer than

logs to logs and polys to polys?

[past panther]

logs to exponentials

polynomials to roots

[spice ivy]

ohhh

that makes sense

[spice ivy]

what about this one

sorry but i need to go over all of them before i do the test tmr

it makes no sense i'm really sorry

[past panther]

this one is unclear whether it's saying stretch around x = 10 or around x = 0

[spice ivy]

oh god

what could i do then?

[past panther]

figure out both

[spice ivy]

Which ones are both even

sorry if i'm being slow

[past panther]

how wonderful, both are answer choices

[spice ivy]

oh wait

so is

a and d the only options?

how do i eliminate like that

[past panther]

you don't

process of elimination is not a catch all

[spice ivy]

oh okay

its A then right?

[past panther]

what was your process

[spice ivy]

foil out and see if it shifts 10 and up 10

is that fair

judging how you responsed i iamgine its D then right

[past panther]

translate up and right
f(x) = |x-10| + 10
stretch around x = 0
f(x) = |x/10 - 10| + 10
flip over y axis
f(x) = |x/10 + 10| + 10
(that's stretching around x = 0)

[spice ivy]

which is none of the options right

[past panther]

i also wrote a process for stretching around x = 10

[spice ivy]

so then i have to try 10?

[past panther]

it is one of the options

[spice ivy]

you're kidding

its not a or d though right

[past panther]

|-a| = |a|

i'm not kidding

[spice ivy]

how could i translate that over to f(x) = |x/10 + 10| + 10
though

[past panther]

wha

you follow the steps

that they tell you to follow

[spice ivy]

yup i get that

Wait so its not A or D right?

i thought with our elimiantion a or d was our only options

how could i elimate my options right off the bat

[past panther]

just

follow the steps

[spice ivy]

stretch horizontally is just 10 right

or 1/10

its 10 right

[past panther]

stretching horizontally around x = 0 by a factor of 10 means replacing all x's with x/10's

[spice ivy]

that forces our answer to be c then though right?

because its -x/10

which the negative we get from reflecting across the y

[past panther]

as |a| = |-a| you can't rely on that

just follow the steps

[spice ivy]

|x| for 1 is |x - 10| + 10 right

then stretch horizontally

|x/10 - 10| + 10

[past panther]

this is in fact equal to c
if this had been c you would have incorrectly eliminated it

[past panther]

yes, correct

then flip

[spice ivy]

x to -x

wait that makes sense

thats what i did

but when i saw how you did it

it was + 10

[past panther]

because i simplified by changing |-a| to |a|

[spice ivy]

which i get your |-a| = |a|

[past panther]

my mistake

[spice ivy]

but

Ohh tat makes sense

thats why i was like its not an answer choice

i'm so sorry

[past panther]

mm

my bad

[past panther]

ok

[spice ivy]

nono you're fine

[past panther]

are you good

[spice ivy]

i really apprecaite the help

yes

i keep getting 2/(x-2)

right to 1/x

is 1/(x - 2)

1/(x/2 - 2)

for stretching horizontally?

[past panther]

yes

[spice ivy]

invert oh god

2/x + 4

then stretch vertically by 2

is that

2(2/x) + 4?

or

2(2/x + 4)?

or neither

[past panther]

multiply everything

4/x + 8

[spice ivy]

ohh so the latter of what i just said

okay perfect

thats only for vertical r ight

horizontal its just the parent thing

and not the up and down shift

4/(x + 2) + 8

[past panther]

horizontal you divide x by the factor of stretch, vertical you multiply everything by the factor of stretch

[spice ivy]

-2(x−10)
over x−8

[spice ivy]

oh okay thank you :)

[rich bear]

@spice ivy has given 1 rep to @past panther

[past panther]

nono don't do it that way

[spice ivy]

how would you do it

[past panther]

leave it as 4/(x+2) + 8

[spice ivy]

thats not inversed though

[past panther]

oh

[spice ivy]

right?

[past panther]

x = 4/(y+2) + 8

[spice ivy]

sorry it says to inverse again

[past panther]

y = 4/(x-8) - 2

[past panther]

im saying dont put it in that form

you want 1 x

so that it's easier to deal with things

[spice ivy]

how could i do that

[past panther]

.

i switched x and y

then solve for y

[spice ivy]

ohh don't even solve for y yet

,w x = 4/(y+2) + 8 solve for y

[worldly imp]

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[spice ivy]

can it do that

wait isn't that what i did

2(x−10)
over x−8

[past panther]

x - 8 = 4/(y+2)
y + 2 = 4/(x-8)
y = 4/(x-8) - 2

this gives you the answer more easily

[spice ivy]

ohh thats fair

and then we multiply this by 2?

[past panther]

compress vertically by factor of 2

[spice ivy]

1/2

ohh so horizontal is opposite to what we think

and vertical is not

right?

[past panther]

yeah

[spice ivy]

1/2 * (4/(x-8) - 2)

[past panther]

vertical is really dividing y by the factor of stretch

[spice ivy]

whole function though right

,w

,w 1/2 * (4/(x-8) - 2)

[past panther]

but as y = f(x) you multiply that over and you get y = factorofstretch*f(x)

[worldly imp]

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Requested by kasimakr#0

[spice ivy]

that makes sense thank you :)

[rich bear]

@spice ivy has given 1 rep to @past panther

[spice ivy]

this isn't any of the optons though

did i screw it up

[past panther]

use this

[spice ivy]

y = 4/(x-8) - 2
right?

y = 1/2 * (4/(x-8) - 2)

[past panther]

dividing by 2 to compress vertically

2/(x-8) - 1

[spice ivy]

Ohh

so it must be a trhen right?

[past panther]

a what?

oh

a

yes

[spice ivy]

answer sorry

Thank you :)

this one

is gonna end up as aroot right?

or is that polys

polys to roots

[past panther]

it's going to end up as an exponential

[spice ivy]

and logs stay logs?

ohh

nvm thank you :)

would be count as one

wouldn't they all be expontentuals

[past panther]

b is polynomial

not exponential

[spice ivy]

oh

[past panther]

exponential has the variable in the exponent

[spice ivy]

that makes sense

log2(x) becomes log2(x9)

[spice ivy]

it should be right

[past panther]

what should

[spice ivy]

vertical compressions

log2(x) becomes log2(x9)

[past panther]

mhm

[past panther]

that's horizontal compression

[spice ivy]

perfect

log2(x9) becomes log2(x9) + 23

oh god

how do i even inverse this

should i convert to expontentual form

[past panther]

log2(9y) + 23 = x
log2(9y) = x - 23
9y = 2^(x-23)

[spice ivy]

ohh that makes sense

9y = 2^(x-23) becomes 9y = -2^(x-23)

right?

[past panther]

yeah

[spice ivy]

it has to be b or c then

right?

to get y we divide 9 on both

or 1/9

its not A

thats for sure

[past panther]

yeah

[spice ivy]

is it C?

[past panther]

yeah

[spice ivy]

Thank you so much

you'er actually the best

for this one

its up 9

and left 2 right

left 2, right?

right as in if its correct

[past panther]

yeah

left 2 up 9

i mean, all of them are possible

you could just shift up 2 down 2 up 9

etc

but thats probably wrong

[spice ivy]

ohh lool

i just its looking for one of each type

using your ideas you taught me is this right

am i getting the hang of it

[past panther]

seems right

[spice ivy]

Loool tysm

this is C right

[spice ivy]

just making sure i get the hang of it

[past panther]

should be division by 11

as it's compress vetically

[spice ivy]

ohh

[spice ivy]

B then?

[past panther]

yeah

[spice ivy]

Thank you :)