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Given: For some real value of $k$:

$$\lim _{ x\rightarrow \infty }{ f(x)=k } $$$$\text{ and }$$$$\lim _{ x\rightarrow -\infty }{ f(x)=k } $$

Which of the following statements is true?

$y=k$ is a horizontal asymptote of $f\left( x \right)$

$y=k$ is a vertical asymptote of $f\left( x \right)$

$\displaystyle\lim_{x\rightarrow k}f(x)=\infty $

$y=k$ is an oblique asymptote of $f\left( x \right)$