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Question

Determine whether the graph of the function is symmetric about the y-axis, the origin, or neither.

y=ex2y = e ^ { - x ^ { 2 } }

Solution

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For finding out whether y=ex2y=e^{-x^{2}} is symmetric about the yy axis or origin we have to check the property of finding function is even or odd

After substitution x=xx=-x we get

y=e(x)2=ex2So here this is fellowf(x)=f(x) Hence function is a even so it is symmetric about y axis \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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