Answer:
a=1, b=-12
Step-by-step explanation:
This is a rational function with a hole at x=3 and a vertical asymptote at x=-4.
The denominator of this rational function must be:
[tex](x - 3)(x + 4)[/tex]
When we expand using the distributive property, we get:
[tex] {x}^{2} + 4x -3 x - 12[/tex]
This simplifies to
[tex] {x}^{2} + x - 12[/tex]
Therefore the graphed rational function is:
[tex]f(x) = \frac{ {x}^{2} - 4x + 3 }{ {x}^{2} + x - 12 } [/tex]
Comparing this to
[tex]f(x) = \frac{ {x}^{2} - 4x + 3 }{ {x}^{2} +a x + b} [/tex]
We have
[tex]a = 1[/tex]
and
[tex]b = - 12[/tex]
