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Sketching a graph of functions and finding asymptotes

1. Approximate real zeros with zoom and trace (on calculator) for the given function.

2. Sketch graph of 2 rational functions as sketching aids, check for intercepts, symmetry, vertical asymptotes, and horizontal asymptotes

3. The management at a factory has found that the maximum number of units a worker can produce in a day is 30. the leaning curve for the number of units N produced per day after a new employee has worked t days is given by N=30[1-e^(kt)]
After 20 days, a worker produced 19 units in 1 day.
a. Find the learning curve for this worker (first hand the value of k)
b. How many days should pass before this worker is producing 25 units/day?


Solution Summary

Using a free graphing tool, the graphs have been made and the solution to all the problems has been derived from them. The second problem involves rational function, while the third one is an application of these concepts. There are 8 graphs in the 5 page solution with more than 300 words.