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

Explanation:

Step1: Analyze first - function

For $y = \frac{x - 6}{x}=1-\frac{6}{x}$, as $x\rightarrow\infty$, $\frac{6}{x}\rightarrow0$, so $y\rightarrow1$.

Step2: Analyze second - function

For $y=\frac{x}{6 - x}=\frac{- (6 - x)+6}{6 - x}=-1+\frac{6}{6 - x}$, as $x\rightarrow\infty$, $6 - x\rightarrow-\infty$, $\frac{6}{6 - x}\rightarrow0$, so $y\rightarrow - 1$.

Step3: Analyze third - function

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

Step4: Analyze fourth - function

For $y=-\sqrt{x - 6}$, as $x\rightarrow\infty$, $\sqrt{x - 6}\rightarrow\infty$, and then $y =-\sqrt{x - 6}\rightarrow-\infty$.

Answer:

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