Of the options that you have offered here, the best answer is “Functional strategies are shaped by corporate strategy.” The other statements are typically the opposite of the actual relationship between the things that are mentioned.
A corporate mission can be defined as a statement about how the firm will compete and in what areas. This mission determines some aspects of a business, but it is itself determined by other things. For example, the corporate mission cannot shape external conditions. Firms may wish they could shape external conditions just by making statements, but they cannot. Instead, external conditions typically help to determine how a firm must compete. Corporate missions are also shaped by the values of the company. The mission is determined by what the firm thinks is important, not the other way around.
By contrast, corporate missions do affect corporate strategies. The corporate mission sets the basic parameters for what the firm will do. The corporate strategy sets out how the firm will go about doing these things. Corporate strategies, in turn, affect functional strategies. Functional strategies are more specific strategies that are set up within the organization to support the corporate strategy.
Thus, it is correct to say that functional strategies are shaped by corporate strategies, but it is incorrect to make the other statements listed here.