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

$Final Answer: The horizontal asymptote is y = - 2, and the vertical asymptote is x = - 3$

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 ： $Final Answer: The horizontal asymptote is y = - 2, and the vertical asymptote is x = - 3$