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Graded Problems Your work on the graded problems should demonstrate your best work. Write up thorough solutions that a reader could follow from start to finish. The original problem, your assumptions and reasoning, your mathematical work, and your answer should all be shown and/or explained clearly. See \"Graded Problem Guidelines\" in the syllabus for more information on expectations and the grading rubric. 1. Write a formula for the rational function shown: 2. Carefully determine the behavior of the function h(x] = LCae ), ) by making numerical (x6) arguments (this means talk about the value of the numerator, denominator, and overall ratio as x approaches these values, rather than describing what the graph looks like). a. T aonoT 3. Ascientist has a beaker containing 30 mL of a solution containing 3 grams of potassium hydroxide. As x approaches -5 from the left As x approaches -5 from the right As x approaches 6 from the left As x approaches 6 from the right As x approaches infinity To this, she mixes a solution containing 8 milligrams per mL of potassium hydroxide. a. Find the concentration if 10 mL of the second solution has been added. Write an equation for the concentration in the tank after adding n mL of the second solution. Find the concentration if 10 mL of the second solution has been added. How many mL of water must be added to obtain a 50 mg/mL solution? What is the behavior as n o0 , and what is the physical significance of this? N