Graph functions

[fresh cosmos]

it is a reciprocal graph

it is a transformation of f(x) = 1/x

the graph f(x) = 1/x has the asimptotes of x = 0 and y = 0

this one has asimptotes of x = -2 and y = 0

you can work out the translation using that

then use that to formulate a function for that graph

[eager linden]

whats the equaiton of f(x) tho

[fresh cosmos]

1/x

[eager linden]

but it crosses at 1 on the y axis

so that cant be the equation

[fresh cosmos]

no this is a translation of that graph

so the equation of this graph is not 1/x

but a translation of 1/x

st it is possible for x = 0

[eager linden]

basically the quesiton is ur given that graph

and its called y=f(x)

and i have yo suggest a possible equation for f(x)

[fresh cosmos]

yh

so by looking at it

it looks like a reciprocal graph right?

[eager linden]

yes

but the normal reciprocal graphs i see dont cross the y axis

this one does

[fresh cosmos]

yh

[eager linden]

and its asymptote is -2

not 0

[fresh cosmos]

yes

but

[eager linden]

well the normal axis

yh

[fresh cosmos]

but

if you take a graph

such as

y = x

[eager linden]

yh

[fresh cosmos]

then translate it by a vector of (2 0)

what is its y-intercept gonna be

[eager linden]

idk

[fresh cosmos]

draw it out

whats y = x

[eager linden]

diagonal line

[fresh cosmos]

then draw the translation

[eager linden]

across origin

upwards

[fresh cosmos]

yh

yh

and is the translation gonna cross the origin?

[eager linden]

no

its gonna cross x axis at -2

i think

idk

[fresh cosmos]

yes

so where will it cross the y axis

[eager linden]

2?

[fresh cosmos]

yh

ok

so now

the same kinda principal applies to the reciprocal graph

y = 1/x doesnt intercept the y axis

but that does not mean its translations will also not intercept the y axis

in fact

[eager linden]

oh ok

[fresh cosmos]

dyk why the graph y = 1/x doesnt intercept the y axis?

[eager linden]

cause those are its asymptotes

[fresh cosmos]

yes but why are they its asymptotes?

[eager linden]

the asymptotes are the axes idk

uh

no clue

[fresh cosmos]

can you do 1/0?

does that have an actual result or is it undefined?

[eager linden]

undefined

[fresh cosmos]

yh

so when x = 0

will there be a value for y?

if the graph is y = 1/x

[eager linden]

no

[fresh cosmos]

exactly

thats why it doesnt cross the y axis. cause the y axis is the line x = 0

however it does tend to the line x = 0

thats just because as the values get smaller what happens to y?

in terms of how its value differs from consequtive x values

[eager linden]

um

idk

[fresh cosmos]

which one is bigger 1/2 or 1/3?

[eager linden]

1/2

[fresh cosmos]

ok

and out of these which is bigger: 1/0.1 or 1/0.2?

[eager linden]

1/0.1

[fresh cosmos]

yh

why is that?

[eager linden]

cause to simplify it

[fresh cosmos]

no

[eager linden]

u can times it by 10

[fresh cosmos]

look at denominators

[eager linden]

and so 10/2 = 5

10/1 = 10

[eager linden]

yh

[fresh cosmos]

without doing any calculations

u can determine 1/2 is bigger than 1/3

without converting them to decimals

because of the denominators

what is it abt the denominators that makes 1/2 bigger than 1/3?

think of it like this: if you have more parts of the same whole, each part will be smaller

[eager linden]

oh yh that makes sense

[fresh cosmos]

hence why as x approaches 0, y approaches infinity

but x never reaches 0

because it is impossible

anyway

back to the q

if the asymptotes have changed

but the shape of the graph remains the same

what kind of transformation are we looking at?

[eager linden]

translation

x axis moves back 2

[fresh cosmos]

yh

[eager linden]

so f(x+2)

[fresh cosmos]

yes

now plug that, x + 2, into the function f(x) = 1/x

what equation do you get?

[eager linden]

wait wdym

[fresh cosmos]

as in

[eager linden]

1/x+2 ?

[fresh cosmos]

yes

so what's your function?

[eager linden]

f(x) = 1/x+2

[fresh cosmos]

wonderful

gj

[eager linden]

so thats the answer?

[fresh cosmos]

yh

[eager linden]

ooh okay makes sense now

thank yu so much

[fresh cosmos]

np