Answer: second option.
Step-by-step explanation:
By definition, a function is even when:
[tex]f(x) = f(-x)[/tex]
Then, knowing this, given the function [tex]f(x)=x^3 +5x+1[/tex] you can substitute [tex]-x[/tex] into this function:
[tex]f(-x)=(-x)^3 +5(-x)+1[/tex]
Now you need to simplify the function. Then you get:
[tex]f(-x)=-x^3 -5x+1[/tex]
In this case, you can see that:
[tex]f(x)\neq f(-x)[/tex]
Therefore, the function [tex]f(x)=x^3 +5x+1[/tex] 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 [tex](-x)^3 +5(-x)+1[/tex] is equivalent to [tex]x^3 +5x+1[/tex]
