SOLUTION: f(x)=-3x^3+2x is this an even odd or nether i just got surger so im on independent study and the book explantion is just confusing me i really need help

Question 129952This question is from textbook algebra 2 prentice hall classics
: f(x)=-3x^3+2x is this an even odd or nether i just got surger so im on independent study and the book explantion is just confusing me i really need help This question is from textbook algebra 2 prentice hall classics

Found 2 solutions by jim_thompson5910, josmiceli:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Remember, a function is even when this equality is true:

and a function is odd when this equality is true:

Lets see if the function is even:

Start with the given equation
Here's :

This is the given equation

Here's :

Replace x with

Simplify

Since does not equal , this means the equation is not true.

Since does not equal , the equation is not an even function.

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Now lets see if the function is odd:

Start with the given equation

Here's :

Remember we solved for this previously

Here's :

Negate the whole function

Distribute the negative and simplify
Since equals , this means the equation is true.

Since equals , the equation is an odd function.

When we graph the equation , we can see if the equation has any symmetry:

and we can clearly see that the equation is not symmetrical with respect to the y axis but is symmetrical with respect to the origin

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Answer:

So is an odd function
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
is an even function because
. The function is reflected
about the y-axis
Let's try your function

So, it's not an even function. Is it an odd function?
is an odd function because

So, your function is odd also
I'll plot it

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