Question

Which function does not have a vertical asymptote?

Answer 1

answer choices A,B,C,D top to bottom :)

Answer 2

is it B? :)

Answer 3

what do you get when you solve the denominator on B

Answer 4

solve 1-x^2 = 0

Answer 5

idk 1+x ?

Answer 6

no solve 1-x^2 = 0 for x

Answer 7

idk i thought it was B just cuz it had x on the top... but yeah i have no idea how to solve... can u pls show me @jim_thompson5910 ? :)

Answer 8

1-x^2 = 0

1 = x^2

x^2 = 1

Keep going

Answer 9

so x=1?

Answer 10

or x = -1

Answer 11

that's not really the point

Answer 12

ok now what? :)

Answer 13

the fact that we got solutions means that there are vertical asymptotes

Answer 14

kk sooo ?? :)

Answer 15

so which denominator, when set equal to 0, won't give you any real solutions?

Answer 16

D??

Answer 17

x+x^2??

Answer 18

x^2+x = 0

x(x+1) = 0

x = 0 or x+1 = 0

Still think this doesn't have any real solutions?

Answer 19

no?? so it has real solutions?

Answer 20

it does, so it can't be that one

Answer 21

idk.. which one is it?? i think its A or B now :P

Answer 22

earlier we showed that 1-x^2 = 0 has 2 real solutions

Answer 23

so its A.??1-2x^2 ??

Answer 24

solve 1-2x^2 = 0 for x

Answer 25

how do i do that?

Answer 26

1-2x^2 = 0

1 = 2x^2

x^2 = 1/2

x = ?? or x = ??

Answer 27

1/4 or -1/4 ??

Answer 28

not really, but you end up with real solutions (it doesn't really matter what they are)

Answer 29

ohhh so my answer is C then? (the last one left haha) ??? 3+x^2 ??

Answer 30

good

Answer 31

kk thanks! :)

Answer 32

hey, now that you are finished, @jim_thompson5910 , why does the denominator needs to have real solutions?

Answer 33

because if the denominator set to zero gives you real solutions, then you'll have vertical asymptotes

Answer 34

if you get complex solutions, you won't have any vertical asymptotes

Answer 35

oooh good point :) thanks!!

Answer 36

yes, that is what you said before, but why?

Answer 37

say you had

y = 1/f(x)

where f(x) is some function

if f(x) = 0 has 2 real roots, then there are 2 real x values that make f(x) equal to zero. This in turn causes a division by zero error which visually graphs the vertical asymptotes

Answer 38

@jim_thompson5910 help with my next one please?? :)
http://openstudy.com/study#/updates/50973b5ae4b02ec0829c1262

Answer 39

if f(x) = 0 has no real solutions (and complex solutions), then there are no real x values that make f(x) equal to zero ---> no division by zero errors ---> no vertical asymptotes

Answer 40

got it thanks

Answer 41

np