Questions: An even function f is one for which f(-x)=f(x) for every x in the domain of f; an odd function f is one for which f(-x)=-f(x) for every x in the domain of f.

Solution Steps

To complete the sentence, we need to identify the types of functions described by the given properties. Specifically, we need to recognize that a function \( f \) for which \( f(-x) = f(x) \) is an even function, and a function \( f \) for which \( f(-x) = -f(x) \) is an odd function.

We need to identify the types of functions based on the given properties:

• A function \( f \) for which \( f(-x) = f(x) \) is called an even function.
• A function \( f \) for which \( f(-x) = -f(x) \) is called an odd function.

Using the identified types of functions, we can complete the sentence as follows:

• An even function \( f \) is one for which \( f(-x) = f(x) \) for every \( x \) in the domain of \( f \).
• An odd function \( f \) is one for which \( f(-x) = -f(x) \) for every \( x \) in the domain of \( f \).

Final Answer