Question

Please help asap and please leave a real answer thank you

Answer 1

`(0.75x - 3)/(x - 1)`

Explanation:

Equation of a rational function is

`(p(x)/(q(x))`

where q(x) isn't zero.

There is a vertical asymptote at

`x = 1`

So this mean that our denomiator must have a zero that occur at x=1.

That zero is

`x - 1`

So our denomiator is

`(p(x))/(x - 1)`

Since our horinzontal asymptote is a non zero value, the numerator must be a linear equation as well.

So our rational function is

`(ax + b)/(x - 1)`

We know the graph pass through (0,3)

So if we apply that logic,

`(a(0) + b)/(0 - 1) = 3`

`(b)/( - 1) = 3`

`b = - 3`

And it passes through (4,0)

`(a(4) + b)/(3) = 0`

`4a + b = 0`

`4a + ( - 3) = 0`

`4a = 3`

`a = (3)/(4)`

So our rational equation is

`(0.75x - 3)/(x - 1)`