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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 coworkers will use for their projects. In particular, you work with a brilliant but forgetil 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 llltime staff and that you have the day o. 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 identication 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 For each entry, enter a single number. First Number: The smallest mintercept (atcoordinate only) Second Number: The largest xintercept (atcoordinate only) Third Number: The largest yintercept (gtcoordinate only] Fourth Number: The vertical asymptote, a: 2 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 coworkers and supervisor. Moving to your desk, you remember that Casey was in charge of creating a password for your computer access. In Casey's standard approach, the password is based on mathematics. You open your notebook with the reminder of this password and see the following Computer password: specify the domain ofthe function f (as) = 135$ | 15. The domain of f (a?) is a: 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 coworkers and supervisor. With your computer now loaded, you bring up the data for your experiment. The data suggests that your experiment can be modeled as by a linear equation. Specically, the volume as a Jnction of time is V {t} = 11 l t. You have been asked to determine the inverse relationship so that the amount of time it will take to reach a given volume can be found. What function do you provide? Enclose numerators and denominators in parentheses. For example, (a: by (1 + n}. HV): @I 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 coworkers and supervisor. You turn to the next task that you were assigned, where an object is moving at a constant speed of 3.8 meters per second (INS). a. Find the distance d that the object as a function of the time spent moving, t. Call this mction d (it). Use *_. an asterisk, for any multiplication and a slash, for any division. (W): @h 11. Find the inverse function by expressing the time spent moving, t, in terms of the distance moved, d. Call this mction t [d]. Use *, an asterisk, for any multiplication and i\