Please complete everything in the attachment. The instructions are all in the attachment. Please do not copy other people's work as this an example exercise. Every piece of info I have is included in the attachment. There are no additional tables or anything else.

Rational Functions Questions Overall Requirements: Justify your solutions. Include the following as needed: Show diagram, Define variables, State formula, theorem, equation or function used, Show substitutions and or steps in solving an equation, State restrictions, State concluding statement, Use correct notation. PLEASE DO NOT INCLUDE IN YOUR SOLUTION: e or In, differentiation, integration. PART A: THE FUNCTIONS INSTRUCTIONS PART 1: Build as few rational functions as possible to satisfy each constraint at least once. Please try to satisfy all constraints in the fewest number of equations. Desmos calculator can be used to test out functions in order to meet the criteria. (Link to desmos: https://www.desmos.com/calculator) Has a hole atx = 4 E. Has a double root at x = -3 B. | Vertical asymptote at x = -2 F. Has a horizontal asymptote y = () C. ' Has a horizontal asympiote y = 2 G. ' Vertical asymptote at x = 1 D. ' Has a single root at the origin H. ' Has a y-intercept at -4 INSTRUCTIONS PART 2: List all of your functions below and number them. Be sure to state which constraints they meet, and justify your choice. Constraints Met Justification (algebraic and/or in words) PART B: INSTRUCTIONS PART 3: Answer the following in complete sentences. Give full and complete explanations. Please thoroughly explain how the equation meets the constraint using appropriate vocabulary, notation, and algebraic evidence with effectiveness. 1. Which constraints pair nicely? 2. Which constraints cannot be paired? 3. Is it possible to satisfy all constraints in 2, 3, or 4 rational functions