Question 2 (20 Points)
Find the vertical and horizontal asymptotes then graph the following function:
\[
y=\frac{1}{x+3}-2
\]

Answer

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Answer

\(\boxed{\text{Final Answer: The horizontal asymptote is } y = -2 \text{, and the vertical asymptote is } x = -3}\)

Steps

Step 1 ：Find the vertical and horizontal asymptotes of the function \(y=\frac{1}{x+3}-2\)

Step 2 ：Analyze the function's behavior as x approaches infinity and as x approaches the value that makes the denominator zero

Step 3 ：Horizontal asymptote: \(y = -2\)

Step 4 ：Vertical asymptote: \(x = -3\)

Step 5 ：\(\boxed{\text{Final Answer: The horizontal asymptote is } y = -2 \text{, and the vertical asymptote is } x = -3}\)