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.

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.
Transcript text: An $\square$ function $f$ is one for which $f(-x)=f(x)$ for every $x$ in the domain of $f$; an $\square$ function $f$ is one for which $f(-x)=-f(x)$ for every $x$ in the domain of $f$.
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Solution

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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 f for which f(x)=f(x) f(-x) = f(x) is an even function, and a function f f for which f(x)=f(x) f(-x) = -f(x) is an odd function.

Step 1: Identify the Types of Functions

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

  • A function f f for which f(x)=f(x) f(-x) = f(x) is called an even function.
  • A function f f for which f(x)=f(x) f(-x) = -f(x) is called an odd function.
Step 2: Complete the Sentence

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

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

Final Answer

even,odd \boxed{\text{even}, \text{odd}}

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