Question 85167
A function is even when this is true


{{{f(x)=f(-x)}}} where in this case {{{f(x)=6x^4+5x-3}}} and {{{f(-x)=6(-x)^4+5(-x)-3}}}


so lets pick any number to plug in for x, say x=2


{{{6(2)^4+5(2)-3=6(-2)^4+5(-2)-3}}} Plug in x=2


{{{6(16)+5(2)-3=6(16)+5(-2)-3}}} Raise 2 and -2 to the 4th power 


{{{96+10-3=96-10-3}}} Multiply


{{{103=83}}} Combine like terms


Since this equation is false, the function is not even


It turns out that if you have a sum of an even function (in this case {{{6x^4}}}) and an odd function (in this case {{{5x}}}) then the function is neither even nor odd. So that means the function {{{f(x)=6x^4+5x-3}}} is neither even nor odd. So it doesn't matter if there is an {{{x^4}}} in the function. If there was only an {{{x^4}}} in the function, and nothing else, then the function would be even.