Question

for which function is it true that y→−∞ as x→∞? y = -√(x - 6) y = x/(x - 6) y = 6/x y = √(x - 6)

Explanation:

Step1: Analyze limit of first function

As $x
ightarrow\infty$, for $y =-\sqrt{x - 6}$, $\sqrt{x-6}
ightarrow\infty$, so $y
ightarrow-\infty$.

Step2: Analyze limit of second function

For $y=\frac{x}{x - 6}=1+\frac{6}{x - 6}$, as $x
ightarrow\infty$, $y
ightarrow1$.

Step3: Analyze limit of third function

For $y=\frac{6}{x}$, as $x
ightarrow\infty$, $y
ightarrow0$.

Step4: Analyze limit of fourth function

For $y=\sqrt{x - 6}$, as $x
ightarrow\infty$, $y
ightarrow\infty$.

Answer:

$y =-\sqrt{x - 6}$