Suppose I have a polynomial of the following form, $$f(x)=\frac{a_1x+a_2x^2+a_3x^3+\cdots+a_nx^n}{b_1x+b_2x^2+b_3x^3+\cdots+b_nx^n}$$ What constraints shall be put on the coefficients and $x$'s so when plotting $f(x)$:
- The line starts above 1.
- If starts below one at some point it goes over 1.
Note coefficients are $a$'s and $b$'s are positive integers.
About point (1) I think the only condition required for $f(x)$ to start above 1 is that $a_1>b_1$?