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

Algebra ->  Rational-functions -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
Remember, a function is even when this equality is true:

f%28x%29=f%28-x%29

and a function is odd when this equality is true:

-f%28x%29=f%28-x%29

Lets see if the function is even:

f%28x%29=-3x%5E3%2B2x Start with the given equation
Here's f%28x%29:

f%28x%29=-3x%5E3%2B2x This is the given equation

Here's f%28-x%29:

f%28-x%29=-3%28-x%29%5E3%2B2%28-x%29 Replace x with -x

f%28-x%29=3x%5E3-2x Simplify

Since -3x%5E3%2B2x does not equal 3x%5E3-2x, this means the equation f%28x%29=f%28-x%29 is not true.

Since f%28x%29 does not equal f%28-x%29, the equation y=-3x%5E3%2B2x is not an even function.


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Now lets see if the function is odd:

y=-3x%5E3%2B2x Start with the given equation

Here's f%28-x%29:

f%28-x%29=3x%5E3-2x Remember we solved for this previously

Here's -f%28x%29:

-f%28x%29=-%28-3x%5E3%2B2x%29 Negate the whole function

f%28-x%29=3x%5E3-2x Distribute the negative and simplify
Since 3x%5E3-2x equals 3x%5E3-2x, this means the equation -f%28x%29=f%28-x%29 is true.

Since -f%28x%29 equals f%28-x%29, the equation y=-3x%5E3%2B2x is an odd function.

When we graph the equation y=-3x%5E3%2B2x, we can see if the equation has any symmetry:
+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+-3x%5E3%2B2x%29+
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 f%28x%29=-3x%5E3%2B2x is an odd function

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
y+=+abs%28x%29 is an even function because
f%28-x%29+=+f%28x%29. The function is reflected
about the y-axis
Let's try your function
f%28x%29+=+-3x%5E3+%2B+2x
f%28-x%29+=+-3%2A%28-x%29%5E3+%2B+2%2A%28-x%29
f%28-x%29+=+-%28-3x%5E3%29+-+2x
f%28-x%29+=+-%28-3x%5E3+%2B+2x%29
f%28-x%29+=+-f%28x%29
So, it's not an even function. Is it an odd function?
y+=+sin%28x%29 is an odd function because
f%28-x%29+=+-f%28x%29
So, your function is odd also
I'll plot it
+graph%28+600%2C+600%2C+-6%2C+6%2C+-8%2C+8%2C+-3x%5E3+%2B+2x%29+