Question

Question was provided via image upload.

Explanation:

Factor the numerator and denominator

Using the Polynomial Factoring and Rational Functions knowledge points

$$ f(x) = \frac{x^2 + x - 6}{x^2 - 6x + 8} = \frac{(x + 3)(x - 2)}{(x - 4)(x - 2)} $$

Identify the removable discontinuity (hole)

Using the Rational Functions knowledge point

$$
LATEXBLOCK0
$$

Identify the vertical asymptote

Using the Vertical Asymptotes knowledge point

$$
LATEXBLOCK1
$$

Answer:

Identify the vertical asymptote and the hole on the graph of the function \(f(x) = \frac{x^2 + x - 6}{x^2 - 6x + 8}\)

There is an asymptote at \(x =\) <blank>4</blank>

There is a hole at (<blank>2</blank>, <blank>\(-\frac{5}{2}\)</blank>)