Question

determine the hole of the function. write it as an ordered pair. f(x) = (4x - 12)/(x^2 + 6x - 27) fractions should be written as n/d

Explanation:

Step1: Factor the numerator and denominator

The numerator $4x - 12=4(x - 3)$. The denominator $x^{2}+6x - 27=(x + 9)(x - 3)$. So $f(x)=\frac{4(x - 3)}{(x + 9)(x - 3)}$.

Step2: Identify the common factor

The common factor between the numerator and denominator is $(x - 3)$. The hole occurs when $x-3 = 0$, i.e., $x = 3$.

Step3: Simplify the function

After canceling out the common factor $(x - 3)$ (for $x
eq3$), we get $y=\frac{4}{x + 9}$.

Step4: Find the y - value of the hole

Substitute $x = 3$ into the simplified function $y=\frac{4}{3+9}=\frac{4}{12}=\frac{1}{3}$.

Answer:

$(3,\frac{1}{3})$