graph the function using transformations, show and state , a) the domain, B) range c) the asymptotes

Question

F(x)= 1/x^2-4

please show work!

Answer 1

I see no use for transformations if F(x) = 1/(x^2-4), so I'll assume you meant what you wrote:

F(x) = (1/x^2) - 4

That is just the graph of 1/x^2, translated 4 units downward.

So, since 1/x^2 has asymptotes x=0 and y=0, F has asymptotes x=0 and y = -4.

Domain is all reals except x=0
Range is all reals except y=-4