SOLUTION: Determine the symmetry (relative to the x-axis, y-axis, and/or origin) of the graph of the function. No need for graph. f(x)= x^3 + x

Question 87302: Determine the symmetry (relative to the x-axis, y-axis, and/or origin) of the graph of the function. No need for graph. f(x)= x^3 + x
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.

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. This means the equation has symmetry with respect to the origin.

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

and we can clearly see that the equation is symmetrical with respect to the origin
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