A math teacher graded student exams on a scale of 0-100. After finishing, the teacher decided to raise the grades. Students could choose one of the following methods to have their grades raised:[br][br][table][tr][td]method 1[/td][td] method 2[/td][td] method 3[/td][/tr][tr][td]Adding 10 points to the grade[/td][td]Increasing the grade by 25%[/td][td]Adding to the grade half [br]the difference between the grade [br]and 100[/td][/tr][/table]Method 1 is shown below in three representations: a computing machine that calculates the updated grade, a graph, and a value table.[br][list][*]Construct computing machines to help students compute their updated grades according to methods 2 and 3. Use the Representation of Functions tool to present graphs and value tables of functions that describe the dependence of the updated grade on the original grade. [/*][*]Suggest a way to determine the best grade-correction method for each student without having to compute their grades using all three methods. [/*][*]What will be the range of grades after the correction?[/*][*]Propose another method for raising the grades, which all students will prefer over the existing methods.[/*][/list][br][br]