Question

$y = \frac{1}{x}$
what is true about the given function?
○ the end behavior as $x \to \infty$ and $x \to -\infty$ is the same.
○ the domain is not all real numbers.
○ it has odd symmetry.
○ all of these are correct

Explanation:

1. End Behavior: For $y=\frac{1}{x}$, as $x \to \infty$, $y \to 0^+$; as $x \to -\infty$, $y \to 0^-$. The end behavior (approaching 0) is the same.
2. Domain: The function is undefined at $x=0$, so its domain is all real numbers except 0, meaning it is not all real numbers.
3. Odd Symmetry: A function is odd if $f(-x) = -f(x)$. For $f(x)=\frac{1}{x}$, $f(-x)=\frac{1}{-x}=-\frac{1}{x}=-f(x)$, so it has odd symmetry.

All three statements are correct.

Answer:

All of these are correct.