Question

Show all work to identify the asymptotes and state the end behavior of the function f(x) = 6x/x-36 (x-36 are both under 6x)

Answer 1

hi mr. jigglypuff314

Answer 2

https://www.ck12.org/book/ck-12-algebra-i-concepts/section/12.3/
if the x values in the numerator and the x values in the denominator have the same power

then the coefficients of those x values (as a fraction) is the asymptote

Answer 3

the asymptotes are x=36 and y = 6 right?

Answer 4

correct

Answer 5

ok but how do u do that

Answer 6

like working it out

Answer 7

Rule 1: you cannot have a value of zero in the denominator

when x=36 in the denominator, what happens?

Answer 8

36 is the denominator?

Answer 9

but its x-36 not x=36

Answer 10

nono

\(\frac{6x}{x-36}\)

what happens when x is equal to 36?

Answer 11

oh then a 0 would be in the denominator

Answer 12

cs 36-36

Answer 13

yes, so that is why there is an asymptote at x=36
it is because having 0 in the denominator is an illegal move in math

Answer 14

ah

Answer 15

ok

Answer 16

so then what abt the 6 asymptote?

Answer 17

but there isnt any exponets

Answer 18

FOR EXAMPLE if you have
\(f(x) = \frac{3x}{2x-7}\) then the asymptote would be 3/2 because 3 is the coefficient of x in the numerator and 2 is the coefficient of x in the denominator

Answer 19

x by itself has an exponent of 1

Answer 20

OHH

Answer 21

OHHH

Answer 22

so what about the end behavior now?

Answer 23

plug in numbers close to those values and identify what happens

like, if you plug in x = 36.5 and compared it to x = 35.5

Answer 24

6*36.5/36.5-36?

Answer 25

yes

Answer 26

6*36.5 = 219

Answer 27

36.5 - 36 = .5

Answer 28

219 / .5 = 438

Answer 29

so x=36.5 has a positive value on the graph

on the other hand x = 35.5 has a negative value on the graph

Answer 30

ah

Answer 31

so i would put

Answer 32

that the end behavior is

Answer 33

positive?

Answer 34

i thought it was asking like yk who they do, as x approaches "blank" f(x) increases/decreases

Answer 35

you see, this is the problem -> as x approaches 36, it is decreasing on the left and increasing on the right

the term here is that it "diverges" but I'm not sure if that is what your teaching is asking for

Answer 36

oh

Answer 37

i could say that it inreases on the right and decreases on the left?

Answer 38

sure, x goes to negative infinity as you approach x=36 from the left
x goes to positive infinity as you approach x=36 from the right

Answer 39

ok

Answer 40

oh wait, I ment "y"

Answer 41

y goes to negative infinity as you approach x=36 from the left
y goes to positive infinity as you approach x=36 from the right

Answer 42

ah ok

Answer 43

thanks so much

Answer 44

u were a very big help

Answer 45

no problemo
glad I could help
it's been a while and tbh I just did a bit of googling lol

Answer 46

LOLL