1. The problem asks for the end behavior of the polynomial function $$p(x) = 4x^8 - 6x^7 + 3x^3 - 10.$$\n\n2. To determine end behavior, focus on the leading term of the polynomial because it dominates as $$x \to \pm \infty$$. The leading term here is $$4x^8$$.\n\n3. The degree of the polynomial is 8, which is even, and the leading coefficient is 4, which is positive.\n\n4. For even degree polynomials with positive leading coefficients, as $$x \to \infty$$, $$p(x) \to \infty$$, and as $$x \to -\infty$$, $$p(x) \to \infty$$.\n\n5. Therefore, the correct end behavior is: as $$x \to \infty$$, $$p(x) \to \infty$$, and as $$x \to -\infty$$, $$p(x) \to \infty$$.\n\nFinal answer: Option A.