Precalculus: It's a Radical, Rational Universe!

Students engage in an exploration of the radical and rational function values. Real world data is explored relating to acceleration due to gravity. Students will graph a given function and use it to find the fall time for different distances from the ground.

Then students will let x represent different values of gravity. Inspection of graphs combined with tracing results in comparisons of times required for the fall of an object in various locations in our solar system. Students identify locations where times of fall will be at a maximum and at a minimum. They will also use the context of the problem to develop appropriate restrictions for the domains and ranges of related graphs.

In the second problem, students explore a problem involving the dilution of a solution to identify maximum and minimum values for concentration of resulting solutions. This problem provides an opportunity to review both horizontal and vertical asymptotes and provides a good example to illustrate limits.