Afunction f ( x ) is said to have a removable discontinuity at x = a if: 1. f is either not defined or not continuous at x = a . 2. f ( a ) could either be defined or redefined so that the new function is continuous at x = a . let f ( x ) = 2 x 2 + 4 x − 48 x − 4 show that f ( x ) has a removable discontinuity at x = 4 and determine what value for f ( 4 ) would make f ( x ) continuous at x = 4 . must define f ( 4 ) = .

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?