2.7: Polynomial and Rational Inequalities
To solve a polynomial inequality, we start by determining the zeros (x­intercepts), which are the values that make the polynomial = 0, aka the "boundary points." Then we determine the behavior of the expression between the boundary points and on each side of them, using a sign chart.
Ex: Solve each of the following inequalities and state your solution in interval notation.
In a rational inequality, our boundary points include not only the zeros of the numerator (i.e. the x­intercepts), but also the zeros of the denominator (i.e. the vertical asymptotes). Ex: Solve each of the following inequalities and state your solution in interval notation.
1
Determine the domain of each function below by solving the inequality "radicand ≥0."
2