Question

This graph represents the function (see picture) a= ___ b= ___

Answer 1

a=1, b=-12

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:

`(x - 3)(x + 4)`

When we expand using the distributive property, we get:

`{x}^(2) + 4x -3 x - 12`

This simplifies to

`{x}^(2) + x - 12`

Therefore the graphed rational function is:

`f(x) = \frac{ {x}^(2) - 4x + 3 }{ {x}^(2) + x - 12 }`

Comparing this to

`f(x) = \frac{ {x}^(2) - 4x + 3 }{ {x}^(2) +a x + b}`

We have

`a = 1`

and

`b = - 12`