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Question

# Determine whether the graph of the function is symmetric about the y-axis, the origin, or neither.$y = e ^ { - x ^ { 2 } }$

Solution

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For finding out whether $y=e^{-x^{2}}$ is symmetric about the $y$ axis or origin we have to check the property of finding function is even or odd

After substitution $x=-x$ we get

\begin{align*} y=e^{-(-x)^{2}}\\ =e^{-x^{2}}\\ \text{So here this is fellow}\\ f(-x) = f(x)\\ \boxed{\text{ Hence function is a even so it is symmetric about y axis }} \end{align*}

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