How do you know if # f(x)=x^3+1# is an even or odd function?

2 Answers
Kevin G.
Dec 15, 2015

Odd.

Explanation:

Quite simply, whether a function is even or odd is whether the degree (the largest exponent) is even or odd.
The degree of #x^3 + 1# is #3#, which is odd, making this an odd function.

mason m
Dec 16, 2015

Neither.

Explanation:

An function is even if: #f(-x)=f(x)#

A function is odd if: #f(-x)=-f(x)#

If #f(-x)=x^3+1#, the function is even.
If #f(-x)=-x^3-1#, the function is odd.

So, find #f(-x)#.

#f(-x)=(-x)^3+1#

#f(-x)=-x^3+1#

This function is neither odd nor even.

A good way to check is by recognizing that even functions are reflections of themselves over the #y#-axis and odd functions are reflections of themselves over the #x#-axis.

This is the graph of #x^3+1#: graph{x^3+1 [-10, 10, -5, 5]}

Notice that if the graph were shifted down one unit (the function #x^3#), the graph would be a reflection of itself over the #x#-axis and would indeed be odd.

Related questions
See all questions in Introduction to Twelve Basic Functions
Impact of this question
1540 views around the world
You can reuse this answer
Creative Commons License