Step-by-step explanation:
If the domain doesn't have 1 or 4 in it. This means 1 and 4 are the zeroes of the denomiator of the rational function.
So
[tex](x - 1)(x - 4)[/tex]
[tex]( {x}^{2} - 5x + 4)[/tex]
So that is the denomiator.
The numerator passes through (-3,3).
Let A represent a posible value of the numerator.
[tex]y = \frac{a}{( {x}^{2} - 5x + 4) } [/tex]
Plug in -3 for x and 3 for y.
[tex]3 = \frac{a}{ - 3 {}^{2} - 5( - 3) + 4 } [/tex]
[tex]3 = \frac{a}{9 + 15 + 4} [/tex]
[tex]3 = \frac{a}{28} [/tex]
[tex]84 = a[/tex]
So one possible function is
[tex]y = \frac{84}{ {x}^{2} - 5x + 4 } [/tex]
