Question

determine the hole of the function. write it as an ordered pair. $f(x)=\frac{6x}{x^{2}+12x}$ fractions should be written as n/d

Explanation:

Step1: Factor the denominator

First, factor the denominator $x^{2}+12x=x(x + 12)$. So the function becomes $f(x)=\frac{6x}{x(x + 12)}$.

Step2: Find the common factor

The common factor of the numerator and denominator is $x$. The function is undefined at $x = 0$ and $x=-12$. But for $x = 0$, we can simplify the function by canceling out the $x$ terms (when $x
eq0$), and we get $f(x)=\frac{6}{x + 12}$.

Step3: Calculate the y - value of the hole

Substitute $x = 0$ into the simplified function $y=\frac{6}{0+12}=\frac{6}{12}=\frac{1}{2}$.

Answer:

$(0,\frac{1}{2})$