Question

given the rational function, $f(x) = \frac{(x-2)(x+1)}{(x-2)}$, what is the $y$-value of the hole?

Explanation:

Step1: Find x-value of the hole

A hole occurs where a factor cancels in numerator/denominator. Set $x-2=0$, so $x=2$.

Step2: Simplify the function

Cancel the common factor $(x-2)$:
$f(x)=x+1$ (for $x
eq2$)

Step3: Calculate y-value

Substitute $x=2$ into the simplified function:
$f(2)=2+1$

Answer:

3