Question

Question was provided via image upload.

Explanation:

Identify the asymptotes from the graph

Using the Rational Function Asymptotes, Vertical Asymptotes, and Horizontal Asymptotes knowledge points

$$
LATEXBLOCK0
$$

Determine the general equation of the rational function

Using the Rational Functions knowledge point

$$
LATEXBLOCK1
$$

Find the value of the parameter a

Using the Rational Functions knowledge point

$$
LATEXBLOCK2
$$

State the final function equation

Using the Rational Functions knowledge point

$$ f(x) = \frac{1}{x - 2} - 2 $$

Answer:

Based on the provided graph of the rational function \(f\):

1. The vertical asymptote is located at \(x = 2\).
2. The horizontal asymptote is located at \(y = -2\).
3. The function passes through the point \((3, -1)\).

Using these features, the equation of the rational function is:

$$f(x) = \frac{1}{x - 2} - 2$$