Manipulating the equation! 
The question asks to manipulate $f(x,y)=e^{-x^2-y^2}$ this equation to make its graph look like the three shapes in the images I attached.
I got the first one: $e^{(-x^2+y^2)}\cos(x^2+y^2)$.
But I have no idea what to do for second and the third one. Please help me.

Is the cosine in the exponent?  In case not, Alpha gives something that looks like the original function

If so, Alpha gives something closer to your second target

