Question

determine the hole of the function. write it as an ordered pair. $f(x)=\frac{x^{2}+10x + 16}{x^{2}+5x - 24}$ fractions should be written as n/d

Explanation:

Step1: Factor the numerator and denominator

Factor $x^{2}+10x + 16=(x + 2)(x+8)$ and $x^{2}+5x - 24=(x + 8)(x - 3)$. So $f(x)=\frac{(x + 2)(x + 8)}{(x + 8)(x - 3)}$.

Step2: Identify the common factor

The common factor is $x + 8$. Set $x+8 = 0$, then $x=-8$.

Step3: Simplify the function

After canceling out the common factor $x + 8$, the simplified function is $y=\frac{x + 2}{x - 3}$.

Step4: Find the y - value of the hole

Substitute $x=-8$ into the simplified function $y=\frac{-8 + 2}{-8 - 3}=\frac{-6}{-11}=\frac{6}{11}$.

Answer:

$(-8,\frac{6}{11})$