Write the equation of a possible rational function that has an asymptote at x = 2, has a
point of discontinuity at x = -2.5, and passes
through (6, -3)

Plz show ALL steps

The graph has a removable discontinuity at x=-2.5 and asymptoe at x=2, and passes through (6,-3)

Step-by-step explanation:

A rational equation is a equation where

where both are polynomials and q(x) can't equal zero.

1. Discovering asymptotes. We need a asymptote at x=2 so we need a binomial factor of

in our denomiator.

So right now we have

2. Removable discontinues. This occurs when we have have the same binomial factor in both the numerator and denomiator.

We can model -2.5 as

So we have as of right now.

Now let see if this passes throught point (6,-3).

So this doesn't pass through -3 so we need another term in the numerator that will make 6,-3 apart of this graph.

If we have a variable r, in the numerator that will make this applicable, we would get

Plug in 6 for the x values.

So our rational equation will be

or

We can prove this by graphing

75

step-by-step explanation: