1. Let's start with polynomial functions. 2. Polynomial inequalities involve finding where a polynomial is greater than or less than zero. 3. Non-linear inequalities are inequalities involving expressions not of degree one, including polynomials and reciprocals. 4. Reciprocal functions have the form $f(x)=\frac{1}{x}$ or similar. 5. To prepare efficiently, focus on understanding factorization, sign charts for inequalities, and behavior of reciprocal functions near zero. 6. Practice problems from Nelson textbook by factoring polynomials, setting up inequalities, and testing intervals. 7. For example, solve $x^2-5x+6>0$ by factoring as $(x-2)(x-3)>0$ and test intervals to find where product is positive. 8. This means $x<2$ or $x>3$. 9. For reciprocal functions like $y=\frac{1}{x}$, understand the vertical asymptote at $x=0$ and horizontal asymptote at $y=0$. 10. Regular practice will build confidence in all these areas. Good luck!