Finding the solution set to a rational inequality is very similar to finding the solution set in a polynomial inequality. The main difference is rational functions can switch from a positive interval to a negative interval without an x-intercept. Use examples to justify your response to each of the following questions:

- How can a rational function switch between positive and negative intervals without an x-intercept?
- Why is this an important factor to think about when solving an inequality?
- How would the intervals of the solution set differ between a polynomial inequality and a rational inequality?