Question

f(x)=e^(1/x)...i need help explaining the graph and how the exponent affects the graph's different portions so when x<0, 00.

Answer 1

type the equation in on wolframalpha.com and u can see the graph. basically when x<0 the function value is getting closer and closer to one as it reaches negative infinity, but it never =1. between 0 and 1, the function gets closer and closer to positive infinity as x gets closer to 0. And when x is greater then zero the function gets closer and closer to 1 as the x value goes to infinity.

Answer 2

that what your looking for bro?

Answer 3

ok so let me see if I understand, so when x<0 the graph is closer to which part of the function 1/x? :/ i think thats how she sort of wants to explain it like which part of the function it is closest to

Answer 4

well hm are there even two parts to the function its not like its e^(x) + 1/x where the two parts would be e^(x) then 1/x..

Answer 5

when x is less then zero the funtion (f(x)) gets closer to negative infinity
so basically in terms of the exponent, as the exponent decreases (as in when x gets smaller and smaller as x<0 indicates) then function f(x), approaches one. So like if x is-50, f(x) will be like .87 for example,and when x is -2000 f(x) woll be like .99, and -50000 f(x) will be like .9999999

Answer 6

theres 1 part to the function

Answer 7

or nvm what were you asking?

Answer 8

so the exponent dominates basically so to speak when x approaches negative infinity because..?

Answer 9

i dont understand your question.k, lets back track. did u read what i wrote about f(x) going to like .9999?

Answer 10

?

Answer 11

yeah

Answer 12

ok did u not understnad it?

Answer 13

think of 1/x. if x is small (like -500000), what will (1/x) =???..
and.......... if x isbig (like 50000000), what will (1/x) =??

Answer 14

hm not sure

Answer 15

well when you have 1/5000 you are putting a larger number on the denomenator so you get a very small fraction? and then if you have 1/-500 you get..

Answer 16

you get a really small negative fraction?

Answer 17

small fraction again just negative

Answer 18

yes. so when the x value gets big. it approaces 0 right.

Answer 19

and when it gets small it a pproaches negative infinity

Answer 20

hm okay just trying to figure out how to say all of this hmm lol

Answer 21

so that answers part of your question

Answer 22

x<0 ... thats where we have negative numbers like -2, -50, -500000. o as we keep mmaking x smaller in x<0 , the overall number for (1/x) get super small too...and thus approaches negative infinity. u gotta be able to grasp that .

Answer 23

no i do now okay, and how come in between 0 and 1 it approaches 0

Answer 24

well when x=1 eaxctly f(x) just equals e^1 right?

Answer 25

e^(1/x) ....e^(1/1) = e^(1) ....1/1 =1

Answer 26

ok

Answer 27

and that is just some number like 2 .7 right. so thats one edge of the boundary. the other edge is 0. cuz it wants x between 0 and 1.

Answer 28

no wait e^(1) is just e not 1 e^(1) is not 1 its e

Answer 29

right

Answer 30

ya e^1=e

Answer 31

when x=0 it says f(x) is undefined..shouldnt it be 1 because any exponent of 0 =1

Answer 32

no. think about it1/x....if x=0, u have 1/0- thats what we call that undefined and you'll get an error on your calculator cuz u cant devide by 0.

Answer 33

5/0. no such thing. 7/0. no such thing. elephant/0. no such thing.

Answer 34

its a hard one to grasp just accept it. 0 is nothing so if you divide something by nothing u get nothing.

Answer 35

right

Answer 36

ight moving on. so between 0 and 1 we have something that equals a number between (undefined and 2.7 right??)

Answer 37

right

Answer 38

if we back it upa bit. and instead of doing1/0. we do 1/say 0.000001 (which is really close to 0. we get a HUGE number for (1/x). right? u get that.

Answer 39

therefore we can say thaas x gets closer to 0 , from 1 (between 0 and 1) the 1/x statement reaches INFINITY. got it?

Answer 40

yeahh

Answer 41

cuz HUGE number is close to Infinity....

Answer 42

can we do f(x)=x^(1/x) (same thing but x instead of e before the exponent)

Answer 43

no my man. e is a constant. its not x.

Answer 44

no no the next one i have to do..is f(x)=x^(1/x)

Answer 45

oh. ythats a little different put that into wolframalpha and u can see the graph you'd get.
ight i gotta peace, i got some lawn work to take care of. peace man hope that was helpful!!

Answer 46

thankssssssssss