Question

The graph of f(x)=1/(x^2-c) has a vertical asymptote at x=3. Find c.

Answer 1

This means the function shouldn't exist at x=3.
So since you have a fraction and fractions don't exist when the bottom is zero, then when is your bottom 0?

Answer 2

Or when is x^2-c=0 for x=3.

Answer 3

Replace x there with 3 and then solve for c.

Answer 4

so c=9?

Answer 5

Perfect. :)
x^2-9 is zero when x=3
which means the function will not exist at x=3 (or even x=-3) but
our objective is completed
Good job!

Answer 6

Thank you!