QUESTION 1 A beverage company has just completed brewing a large batch of tea (1000 gallons). They will be adding sweetening to the tea, then bottle it and prepare it for distribution. a) Suppose 30 gallons of corn syrup is added to the mixture as a sweetener. 1. Whatis the ratio of tea to corn syrup in the mixture? 2. What if 80 gallons of corn syrup were added instead? 3. Whatif 130 gallons of corn syrup were added instead? b) Define a function f whose input x is the amount of corn syrup added (in gallons) and whose output R is the ratio of tea to corn syrup in the mixture. c) What is the practical domain for the function you defined? d) Complete the given table for values of this function: e) What happens as x 01 ? Why does this make sense? QUESTION 2 Suppose f(x) = i% a) Find the horizontal intercepts of f b) Find the vertical intercept of f c) Find the vertical asymptote of the graph of f d) Find the horizontal asymptote of the graph of f. e) Graph f(x) 8 T 6 6 -4 -3 2 +1 0 1 2 3 4 b 6 T 8 QUESTION 3 A ball is thrown upward. It's height above the ground, in feet, can be modeled by the function f(t) = 3t? + 18t, where t is the number of seconds elapsed since the ball has been thrown. During which time interval is the ball more than 15 feet above the ground