What is the maximum number of real roots for the function \(f(x) = x^5 - 4x^3 + 2x^2 - 8\)?

Step 1 ：To find the maximum number of real roots of a polynomial function, we can use the Fundamental Theorem of Algebra which states that a polynomial of degree \(n\) has exactly \(n\) roots, counting multiplicity.

Step 2 ：The degree of the polynomial function \(f(x) = x^5 - 4x^3 + 2x^2 - 8\) is 5, which is the highest power of \(x\).

Step 3 ：Therefore, the maximum number of real roots for the function is 5.