Question

Please help me!
The graph of f(x)= 1/(x^2-c) has a vertical asymptope at x=3. Find C.

Answer 1

If a function has a vertical asymptote at a particular value of x, it means that its value if infinite at that point. so, how can this equation:

1/(x^2-c)

become infinite in value - can you guess what the condition must be?

Answer 2

*value is infinite

Answer 3

any number greater than 0?

Answer 4

if 1/z is infinite, then what does that tell you about z?

Answer 5

i.e. what number can you divide by in order to infinity?

Answer 6

1?

Answer 7

1/1 = infinity?

Answer 8

I have no clue...

Answer 9

ok, think about this - what is 1/0.5 = ?

Answer 10

2

Answer 11

good. now what is 1/0.05 = ?

Answer 12

20

Answer 13

so - can you see that as the denominator becomes smaller then 1 divided by that number becomes bigger

Answer 14

yes

Answer 15

so think about this - what is the smallest value that the denominator could become?

Answer 16

0.5, 0.05, 0.005, 0.0005, ..., what value will we tend towards?

Answer 17

.0005

Answer 18

if we keep smaking the denominator smaller and smaller - what will it eventually become?

Answer 19

*making

Answer 20

infinate

Answer 21

no - that is making the denominator bigger and bigger

Answer 22

all I am getting from this is that the answer needs to be .0000000000000000000000000000000000005

Answer 23

what is the smallest positive number you can think of?

Answer 24

1

Answer 25

including zero

Answer 26

0

Answer 27

yes, so 1/0 will be infinity

Answer 28

so, in your equation, you need:\[x^2-c=0\]at x=3

Answer 29

so C=0?

Answer 30

first replace x^2 by 3^2 - what do you get?

Answer 31

why are we replacing that and where did you get that option

Answer 32

your question says that there is an asymptote at x=3

Answer 33

so we need to replace x with 3 in the equation for f(x)

Answer 34

so is c zero or not?

Answer 35

correct - c is not zero

Answer 36

so what is c?

Answer 37

follow the steps I have outlined above and you should be able to solve for c.

Answer 38

i appreciate you taking forever to explain this to me, but i have about 500 more problems to do and not much time to do them.

Answer 39

@asnaseer i think that asymptope means approcing to a value but not reaches to it then it is not necessary to be infinity :)

Answer 40

@Aperogalics The value of f(x) at x=3 will be infinite if f(x) has a vertical asymptote at x=3

Answer 41

no @asnaseer i m not going with this question i m talking about asymptote only :)

Answer 42

general :)

Answer 43

of course in general asymptotes do not have to be vertical

Answer 44

I just need to know C

Answer 45

@stevenchannell substitute x=3 into this equation:\[x^2-c=0\]and then solve to find c.

Answer 46

no my mean to say not by vertical or horizontal or inclined but reaching to infinity is not the case which mean asymptote:)

Answer 47

oh I see what you are trying to say now - yes - you are right :)

Answer 48

c=9?

Answer 49

perfect! @stevenchannell

Answer 50

my advise to you would be that it is better to take things slowly and understand the subject matter rather than trying to rush through lots of questions. :)

Answer 51

yes I understand that, but all my work is online work and I will be leaving out of town for the next week