Question

determine the hole of the function. write it as an ordered pair. f(x) = \frac{x + 4}{x^{2}+7x + 12} fractions should be written as n/d

Explanation:

Step1: Factor the denominator

Factor \(x^{2}+7x + 12\) as \((x + 3)(x+4)\). So \(f(x)=\frac{x + 4}{(x + 3)(x + 4)}\).

Step2: Identify the common factor

The common factor of the numerator and denominator is \(x + 4\). Set \(x+4=0\), we get \(x=-4\).

Step3: Simplify the function

After canceling out the common factor \(x + 4\) (for \(x
eq - 4\)), \(f(x)=\frac{1}{x + 3}\).

Step4: Find the y - value of the hole

Substitute \(x=-4\) into the simplified function \(y=\frac{1}{-4+3}=-1\).

Answer:

\((-4,-1)\)