Directions: Complete all of the following problems. Please write neatly. In addition to your answers, you will also be graded on the accuracy of your work and the correctness of your mathematical notation (if applicable}. For Questions 13, rewrite the given question or statement by lling in the blanks. Question 1 Is there a real number whose square is 2 '2' {a} Is there a real number T such that i\" [-5) Does there exist such that r2 = 2 ? Question 2 Given an two distinct real numbers, there is a real number between them. 3' [Note: Two numbers are distinct if they are not equal.) {a} For distinct real numbers I and y, there exists such that [-5) lGiven two , there exists a such that c. c: c (1 f3. Question 3 For e1I..rer;I..r function ffc}, if f[:r} is cubic, then ffz} has at most three roots. [Note: A cubic function is a function of the form at} 2 11.13 + 312 + or + cf, and a moi of a function at} is a solution to the equation ffz} = G.) {a} All cubic functions [-5) If a function is cubic, then {c} For every cubic function at}, Question 4 Rewrite the following statement without using 1variables. Then, give an exam ple that shows the statement is true. There exist two real numbers .1: and y such that :r + 3;