Introduction You have received an internship at Curie Chemical, which specializes in chemical engineering. As part of your internship, you are responsible for several early states of work that your co-workers will use for their projects. In particular, you work with a brilliant but forgetful individual, Casey, who keeps notes all over the office with reminders of work to be done and even their passwords. In order to keep notes private, Casey would often write in terms of mathematical formulas in hopes that anyone who came upon them would not be able to decipher the writing. Your first week is going well, and you are looking forward to wrapping up some work before the weekend. As you arrive at the office on Friday morning, you are surprised at how quiet it is. You then remember that today is a company offsite for all full-time staff and that you have the day off. Before you enjoy your suddenly free Friday, you decide to take one last look at your work to make sure everything is in a good place for next week. The Entrance Keypad You walk up to the main entrance and remember that a identification number is required to enter. This keypad allows for the entry of any number, including negative values. Fortunately, you remember that Casey left a hint for this password that you wrote down in your notebook. You open your bag and find the below information written in your notes: Find the intercepts and the vertical asymptote of f(x)=x^2−11x−12/x−6 For each entry, enter a single number.
First Number: The smallest x -intercept (x -coordinate only).
Second Number: The largest x -intercept (x -coordinate only).
Third Number: The largest y -intercept (y -coordinate only).
Fourth Number: The vertical asymptote, x= .
Explain, in your own words and with your own work, how you arrived at this result. Be sure to explain using appropriate mathematical concepts to support your co-workers and supervisor.
