Question

The graph of f(x)=1 overx^2-c has a vertical asymptote as x=3. Find c. I honestly do not know where to begin...

Answer 1

if x = 3 is a vertical asymptote, then plugging in x = 3 into the function should result in a division by zero error

ie...the denominator x^2 - c should be 0 when x = 3

Answer 2

x^2 - c

3^2 - c ... plug in x = 3

9 - c

this should be zero, so 9 - c = 0 ----> c = ???

Answer 3

If i started with 9-c=0 it would lead to -c=-9 right? Then i could do (-1)c=(-1)9, so then my answer would be c=9 ?

Answer 4

you nailed it

Answer 5

You are a lifesaver :) Thank you

Answer 6

side note: x = 3 is just one of the two vertical asymptotes of 1/(x^2 - 9)

you're welcome