15. which of the following is true regarding the graph of f(x)=1/x? there is no horizontal asymptote. the…

Explanation:

Step1: Analyze domain

The function $f(x)=\frac{1}{x}$ is undefined when $x = 0$. So the domain is all real - numbers except $x = 0$, not all real numbers.

Step2: Analyze x - intercept

To find the x - intercept, set $y = 0$. So $0=\frac{1}{x}$, which has no solution since $1\neq0$ for any real $x$. So there is no x - intercept at $(0,0)$.

Step3: Analyze horizontal asymptote

As $x\rightarrow\pm\infty$, $y=\frac{1}{x}\rightarrow0$. So $y = 0$ is a horizontal asymptote.

Step4: Analyze range

Let $y=\frac{1}{x}$, then $x=\frac{1}{y}$. Since $x$ can take any non - zero real value, $y$ can take any non - zero real value. So the range is all real numbers, $y\neq0$.

Answer:

The range is all real numbers, $y\neq0$