Question: Given

\(f\left( x \right)=\frac{1}{\sqrt{2\pi }}{{e}^{-\frac{{{x}^{2}}}{2}}}\)

1. Determine whether the graph of \(f\) is symmetric about the \(x\) -axis, \(y\) -axis, or the origin.
2. Find the intervals on which \(f\) is increasing, and those on which \(f\) is decreasing.
3. Find the coordinates of all relative extrema of \(f\).
4. Find \(\lim _{x \rightarrow-\infty} f(x)\) and \(\lim _{x \rightarrow \infty} f(x)\).
5. Find the intervals on which the graph of \(f\) is concave up, and those on which \(f\) is concave down.
6. Find the coordinates of all points of inflection.
7. Find the intercepts.
8. Find the vertical and non-vertical asymptotes.
9. Sketch the graph of \(f\).
10. Find all absolute extrema.

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