Sketch the graph of a function g(y) such that the one-parameter family of differential equations dy/dt = g(y)+ α satisfies all of the following properties:
• For all α ≤ −4, the differential equation has one sink and no other equilibria.
• For all α ≥ 4, the equation has one sink and no other equilibria.
• For α = 0, the differential equation has exactly six equilibria.
[There are many possible functions g(y) that satisfy these conditions. Sketch just one graph.]
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