Question

could the three graphs be antiderivatives of the same function? are the three graphs antiderivatives of the same function? yes no

Explanation:

Step1: Recall the property of antiderivatives

If \(F(x)\) and \(G(x)\) are antiderivatives of the same function \(f(x)\), then \(F(x)-G(x)=C\), where \(C\) is a constant. Geometrically, the graphs of two antiderivatives of the same function are vertical translations of each other.

Step2: Analyze the given graphs

Looking at the three graphs, we can observe that they are vertical translations of each other. For any two of the graphs, the vertical distance between corresponding points is constant.

Answer:

Yes