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

Answer:

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

Explanation:

Step1: Analyze option A

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

Step2: Analyze option B

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

Step3: Analyze option C

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

Step4: Analyze option D

For $y=\frac{x - 6}{x}=1-\frac{6}{x}$, as $x\to\infty$, $y\to1$.