Question

Which statement best describes how to determine wether f(x)=x^3 +5x+1 is an even function

Answer 1

Answer: second option.

Explanation:

By definition, a function is even when:

`f(x) = f(-x)`

Then, knowing this, given the function
`f(x)=x^3 +5x+1` you can substitute
`-x` into this function:

`f(-x)=(-x)^3 +5(-x)+1`

Now you need to simplify the function. Then you get:

`f(-x)=-x^3 -5x+1`

In this case, you can see that:

`f(x)\\eq f(-x)`

Therefore, the function
`f(x)=x^3 +5x+1` is not even.

As you observed in the procedure above, the statement that best describes how to determine whether the given function is even is:

Determine is
`(-x)^3 +5(-x)+1` is equivalent to
`x^3 +5x+1`