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Chapter 2: Q. 8 (page 89)

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.

Short Answer

Expert verified

Aneven 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 by step solution

01

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.

02

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 .

03

final answer

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

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

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Most popular questions from this chapter

In Problems 33– 44, determine algebraically whether each function is even, odd, or neither.

g(x)=x2+3x2-1

True or False The domain of the function f(x)=x2-4xis{x|x≠±2}.

Match each graph to its function.

A. Constant function

B. Identity function

C. Square function

D. Cube function

E. Square root function

F. Reciprocal function

G. Absolute value function

H. Cube root function

Find the following for each function:

fx=3xx2-1

Part (a):f2

Part (b):f-2

Part (c):f-x

Part (d):-fx

Part (e):fx-2

Part (f):f2x

Graph the function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. Verify your results using a graphing utility.

g(x)=x3+1
See all solutions

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