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.
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 $f$.
Solution
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.
Step 1: Identify the Types of Functions
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.
Step 2: Complete the Sentence
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.