which of the following is a key attribute of the reciprocal function f(x)=1/x? (1 point) as x is approaching…

which of the following is a key attribute of the reciprocal function f(x)=1/x? (1 point) as x is approaching -∞, the function f(x)=1/x approaches 1. the point (0,0) is on the graph of the function. the vertical asymptote of the reciprocal function is the line y = 0. as x is approaching 0 from the left, the function f(x)=1/x approaches -∞.

which of the following is a key attribute of the reciprocal function f(x)=1/x? (1 point) as x is approaching -∞, the function f(x)=1/x approaches 1. the point (0,0) is on the graph of the function. the vertical asymptote of the reciprocal function is the line y = 0. as x is approaching 0 from the left, the function f(x)=1/x approaches -∞.

Answer

Explanation:

Step1: Analyze limit as x approaches -∞

For $y = \frac{1}{x}$, as $x\to-\infty$, $\lim_{x\to-\infty}\frac{1}{x}=0$, not 1.

Step2: Check if (0,0) is on the graph

The function $y=\frac{1}{x}$ is undefined at $x = 0$ since $\frac{1}{0}$ is undefined, so $(0,0)$ is not on the graph.

Step3: Identify vertical - asymptote

The vertical asymptote of $y=\frac{1}{x}$ is $x = 0$, not $y = 0$. The horizontal asymptote is $y = 0$.

Step4: Analyze limit as x approaches 0 from the left

As $x\to0^{-}$, $\lim_{x\to0^{-}}\frac{1}{x}=-\infty$.

Answer:

As x is approaching 0 from the left, the function $f(x)=\frac{1}{x}$ approaches $-\infty$.