For each function fi determine whether it is injective but not surjective, surjective but not injective, bijective, or neither injective nor surjective. explain why. (1) fi: r30 + r with fi() = ? for all z ero, where ro = {1 er > 0} = (0,00). (2) f2: ro ro with f(x) = r2 for all r er> 0. (3) f3: r → ro with f(x) = r for all r e r. (4) : r r with f(x) = 10" for all x er. (here 10stands for 1064), not (10" hint. your solution may follow this example: let fs: r → r with f(x) = x for all r € r. then fs is neither injective nor surjective. it is not injective because fs(1) = f(-1) while 1*-1. it is not surjective because there is no r e r such that = -2

In one day there are too high tides into low tides and equally spaced intervals the high tide is observed to be 6 feet above the average sea level after six hours passed a low tide occurs at 6 feet below the average sea level in this task you will model this occurrence using a trigonometric function by using x as a measurement of time assume the first high tide occurs at x=0. a. what are the independent and dependent variables? b. determine these key features of the function that models the tide: 1.amplitude 2.period 3.frequency 4.midline 5.vertical shift 6.phase shift c. create a trigonometric function that models the ocean tide for a period of 12 hours. d.what is the height of the tide after 93 hours?