I'll solve this "Check for the Functions" worksheet by examining each relation to determine if it's a function. A relation is a function if and only if each input value (x-value) is paired with exactly one output value (y-value).
Let me go through each problem one by one:
Problem 1:
- Input values: 2, 3, 4, 5
- Each input has exactly one output: 2→6, 3→7, 4→8, 5→9
- This IS a function ✓
Problem 2:
- Input values: -4, -3, 0
- Each input has exactly one output: -4→6, -3→5, 0→1
- This IS a function ✓
Problem 3:
- Input values: 2, 0, -1, 3
- Each input has exactly one output: 2→8, 0→12, -1→14, 3→10
- This IS a function ✓
Problem 4:
- Input values: -4, -5, -11, -12
- Each input has exactly one output: -4→-5, -5→-11, -11→-12
- This IS a function ✓
Problem 5:
- Input values: 1, 2, 3, 4
- Each input has exactly one output: 1→1, 2→4, 3→9, 4→16
- This IS a function ✓
Problem 6:
- Input values: 4, 8, 10, 15
- Each input has exactly one output: 4→12, 8→14, 10→15, 15→20
- This IS a function ✓
Problem 7:
- Input values: -6, -2, 0, 4
- Each input has exactly one output: -6→4, -2→0, 0→4, 4→4
- Note: Even though the output 4 appears multiple times, each input still has only one output.
- This IS a function ✓
Problem 8:
- Input values: -10, -6, 2, 4
- Each input has exactly one output: -10→-6, -6→-4, 2→-4, 4→-2
- This IS a function ✓
Problem 9:
- Input values: -1, 0, 1, 2
- Each input has exactly one output: -1→0, 0→-1, 1→-2, 2→-3
- This IS a function ✓
Problem 10:
- Input values: -30, -16, 16, 30
- Each input has exactly one output: -30→10, -16→20, 16→20, 30→10
- This IS a function ✓ (Note: Again, even though outputs repeat, each input has only one output)
Problem 11:
- Input values: -8, 6, 7, -6
- Each input has exactly one output: -8→-3, 6→2, 7→0, -6→-2
- This IS a function ✓
Problem 12:
- Input values: 7, 2, -6, -4, 0
- Each input has exactly one output: 7→-3, 2→3, -6→0, -4→0, 0→0
- This IS a function ✓ (Even though output 0 appears multiple times, each input has only one output)
All 12 relations are functions because in each case, every input value is paired with exactly one output value.
The solution is to mark all 12 boxes with a checkmark (✓).
Parent Tip: Review the logic above to help your child master the concept of functions math worksheet.
