We want to determine the end behavior of the graph of the given polynomial function. To do so, we will pay close attention to the leading term ax^n, where a is the leading coefficient and n is the degree of the polynomial. Let's consider the given polynomial function. Note that it is already written in standard form.
f(x)= 1x^8 -8x^4+6x^2
We can see above that the leading coefficient is 1 and the degree is 8. Let's now see how the leading coefficient and degree affect the end behavior of the graph of a polynomial function.
Since 1>0 and 8 is an even number, the end behavior of the given function is up and up.
