End Behavior 8Ee3C2

1. **State the problem:** We want to find the end behavior of the function $$g(x) = -4x^3 + 5x^6 + 3x^2 - 8$$. 2. **Recall the rule for end behavior:** The end behavior of a polynomial function is determined by its leading term, which is the term with the highest power of $$x$$. 3. **Identify the leading term:** In $$g(x)$$, the term with the highest power is $$5x^6$$. 4. **Analyze the leading term:** Since the leading term is $$5x^6$$, and the coefficient $$5$$ is positive, and the degree $$6$$ is even, the end behavior is: - As $$x \to +\infty$$, $$g(x) \to +\infty$$. - As $$x \to -\infty$$, $$g(x) \to +\infty$$. 5. **Summary:** The function grows very large positively on both ends because the highest degree term dominates and is positive with an even exponent. **Final answer:** $$\lim_{x \to \pm\infty} g(x) = +\infty$$