Chapter 3 - Section 3.4 - Polynomial Functions: Graphs, Applications, and Models - 3.4 Exercises - Page 331: 27

If $x\to \infty$, then $y\to -\infty$ If $x\to -\infty$, then $y\to -\infty$

$$f(x)=3+2x-4x^2-5x^{10}$$ Reorder: $$f(x)=-5x^{10}-4x^2+2x+3$$ Since degree of polynomial is even ($10$) and leading coefficient is negative ($-5$), then end behavior is: If $x\to \infty$, then $y\to -\infty$ If $x\to -\infty$, then $y\to -\infty$