Q. 8 - Precalculus Enhanced with Graphing Utilities

Question

Concepts and Vocabulary

A(n)  ------------ function f is one for which f(-x)=f(x) for every x in the domain of f 

 a(n) ________ function f is one for which f(-x)=-f(x)  for every x in the domain of f.

Step-by-Step Solution

Answer

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.

Step 1: Given information

A(n)  ------------ function f is one for which f(-x)=f(x) for every x in the domain of f 

 a(n) ________ function f is one for which f(-x)=-f(x)  for every x in the domain of f.

Step 2:

To find whether the given function is odd or even function , we replace x  with -x in f(x)

If f(-x)= f(x) original function then it is an even function . 

If f(-x)=-f(x)   then it is an odd function . 

Step 3: final answer

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.