Visualizing the Family of Anti-Derivatives

A. It represents the set of all possible functions whose derivative is f′(x)=2x, differing only by a constant.

B. It is the specific function for the derivative f′(x)=2x.

C. It is the only function whose derivative is f′(x)=2x.

D. It is the derivative of all functions with a constant term.

A. Because g(x) is the same as f(x), only with a constant difference.

B. Because g′(x)=f′(x), meaning they have the same rate of change.

C. Because g(x) and f(x) are identical functions.

D. Because g(x) is the second derivative of f(x).

A. The derivative of g(x), which is g′(x)=2x.

B. The function g(x)=x2+8.

C. The rate of change of g(x).

D. The constant term of g(x).

A. A function whose derivative is g(x).

B. The constant term added to g(x).

C. The value of g(x) at a specific point.

D. A function with an arbitrary constant added to g(x).

A. Because the process of finding an antiderivative introduces an arbitrary constant, so we have a family of functions.

B. Because the linear function has an infinite number of derivatives.

C. Because the derivative of a function always results in a constant.

D. Because we can ignore the constant term in the antiderivative.