Does a corporation in the state of California have to serve a business purpose/function or have a motive for profit?

The corporation does not have to state its specific purpose in its Articles of Incorporation. However, the law requires the Articles of Incorporation to state that the purpose of the corporation is to engage in any lawful act or activity for which a corporation may be organized under the General Corporation Law of California other than the banking business, the trust company business or the practice of a profession permitted to be incorporated by the California Corporations Code. Likewise, a limited liability company does not have to state its purpose in its Articles of Organization. However, the law requires that the Articles of Organization state that the purpose of the limited liability company is to engage in any lawful act or activity for which a limited liability company may be organized under the California Revised Uniform Limited Liability Company Act.

No. Corporations and LLCs can be formed for reasons other than conducting business and making a profit.

In California you may also have various types of nonprofit corps (public benefit, charitable, religious) or some newer corporate entities: "benefit corporations" and "flexible purpose corporation" - all of which deviate from the traditional corporate model where the fundamental tenet is that the corporation exists to maximize shareholder value, which generally means a pursuit of profit, even if the corporate purpose as stated in the articles of incorporation may be of a general purpose statement as noted in the other posts. Under the traditional corporate model, then failure to pursue shareholder value may leave the entity (or directors) liable for breaches of the duty of care; although in reality such suits rarely succeed because of the mechanics of how derivative suits work.