This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Identify the range of x values. The interval is -1 x 6. Since these are linear functions, we will use integer values for x within this interval: x \-1, 0, 1, 2, 3, 4, 5, 6\ Step 2: Calculate the values for the first function, y = 4-x, for each x in the interval. For x=-1: y = 4 - (-1) = 4+1 = 5 For x=0: y = 4 - 0 = 4 For x=1: y = 4 - 1 = 3 For x=2: y = 4 - 2 = 2 For x=3: y = 4 - 3 = 1 For x=4: y = 4 - 4 = 0 For x=5: y = 4 - 5 = -1 For x=6: y = 4 - 6 = -2 Step 3: Calculate the values for the second function, y = 3x-8, for each x in the interval. For x=-1: y = 3(-1) - 8 = -3 - 8 = -11 For x=0: y = 3(0) - 8 = 0 - 8 = -8 For x=1: y = 3(1) - 8 = 3 - 8 = -5 For x=2: y = 3(2) - 8 = 6 - 8 = -2 For x=3: y = 3(3) - 8 = 9 - 8 = 1 For x=4: y = 3(4) - 8 = 12 - 8 = 4 For x=5: y = 3(5) - 8 = 15 - 8 = 7 For x=6: y = 3(6) - 8 = 18 - 8 = 10 Step 4: Construct the table of values. The completed table is: |c|c|c| x & y = 4-x & y = 3x-8 \\ -1 & 5 & -11 \\ 0 & 4 & -8 \\ 1 & 3 & -5 \\ 2 & 2 & -2 \\ 3 & 1 & 1 \\ 4 & 0 & 4 \\ 5 & -1 & 7 \\ 6 & -2 & 10 \\ 3 done, 2 left today. You're making progress.