Solving and Graphing Polynomial and Rational Inequalities

The video tutorial covers graphing and solving inequalities, including polynomial and rational inequalities. It begins with a basic introduction to inequalities, explaining the difference between equations and inequalities. The tutorial then demonstrates how to solve polynomial inequalities using number lines and test points. It also covers graphing two-variable inequalities by treating them as equations and shading the solution area. Finally, the video explains rational inequalities, focusing on finding x-intercepts and vertical asymptotes. The tutorial concludes with a comprehension check.

What is the definition of an inequality?

How do you solve the inequality x squared plus 6x is less than -5?

What does it mean to test points in the context of solving inequalities?

What steps are involved in graphing the inequality y is greater than or equal to x plus 2?

What is the significance of shading in the coordinate plane when graphing inequalities?

Explain how to find the solution to a rational inequality.

Describe the process of determining the intervals where a function is above the line y equals zero.