Question 271865: f(x)=7x^3+4x-2 is this even or an odd or neither..
f(-x)=7(-x)^3+4(-x)-2
f(-x)=-7x^3-4x-2
which is neither.. but im not sure please help???
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! Here's more information than you ever wanted to know about even and odd functions.
http://en.wikipedia.org/wiki/Even_and_odd_functions
The basic information is this:
A function is even if f(x) = f(-x)
Geometrically, the graph of an even function is symmetric with respect to the y-axis, meaning that its graph remains unchanged after reflection about the y-axis.
A function is odd if -f(x) = f(-x)
Geometrically, the graph of an odd function has rotational symmetry with respect to the origin, meaning that its graph remains unchanged after rotation of 180 degrees about the origin.
If a graph is neither even or odd, then it will not have either of the geometric properties mentioned above.
Look at the three graphs in that link to see an example of an even function, an odd function, and a function that is neither even or odd.
Before I even test your function, I will graph it to see what it looks like.
Since it starts with x^3, then I would tend to think of it as more odd than even.
The graph of your function looks like this:
From the graph it looks like it is neither even or odd.
It is not symmetric about the y axis.
It does not look symmetric about the origin.
If it was, then the y-intercept would have been the point (0,0) which it is not.
To be sure we'll give it the tests.
f(x) = 7x^3+4x-2
f(-x) = 7(-x)^3 + 4*(-x) - 2 which becomes -7x^3 -4x -2
-f(x) = -7x^3 - 4x + 2
f(x) does not equal f(-x) so the function is not even.
-f(x) does not equal f(-x) so the function is not odd.
It has to be neither.
An example of an even function is:
f(x) = x^2
f(-x) = (-x)^2 = x^2
Since f(-x) = f(x), then the function is even.
An example of an odd function is:
f(x) = x^3
f(-x) = (-x)^3 = -x^3
-f(x) = -x^3
Since -f(x) = f(-x), then the function is odd.
Based on the tests we made on your function, and based on what the graph is showing, it's clear that your function is neither even nor odd.
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