Check for the Functions | Worksheet - Free Printable

I'll solve this problem by checking each relation to determine if it is a function. A relation is a function if each input value (x) has exactly one output value (y).

Let me go through each problem one by one:

Problem 1:
- Input values: 2, 3, 4, 5
- Each input maps to exactly one output: 2→4, 3→6, 4→8, 5→10
- This IS a function.

Problem 2:
- Input values: -4, -3, 0
- Each input maps to exactly one output: -4→6, -3→5, 0→1
- This IS a function.

Problem 3:
- Input values: 2, 0, -1, 0 (note that 0 appears twice)
- The input 0 maps to both 12 and 10 (two different outputs)
- This is NOT a function (since one input has multiple outputs).

Problem 4:
- Input values: -4, -5, -6, -11, -12
- Each input maps to exactly one output: -4→-5, -5→-6, -6→-11, -11→-12
- This IS a function.

Problem 5:
- Input values: 2, 3, 4, 5
- Each input maps to exactly one output: 2→7, 3→8, 4→9, 5→10
- This IS a function.

Problem 6:
- Input values: 5, 7, 10, 15
- Each input maps to exactly one output: 5→10, 7→14, 10→20, 15→30
- This IS a function.

Problem 7:
- Input values: -6, -4, 0, 2, 4
- Each input maps to exactly one output: -6→4, -4→2, 0→0, 2→-2, 4→-4
- This IS a function.

Problem 8:
- Input values: -10, -6, 0, 2, 4
- Each input maps to exactly one output: -10→6, -6→2, 0→-2, 2→-4, 4→-6
- This IS a function.

Problem 9:
- Input values: -1, 0, 2, 4
- Each input maps to exactly one output: -1→-6, 0→-4, 2→0, 4→8
- This IS a function.

Problem 10:
- Input values: -30, -15, 15, 30
- Each input maps to exactly one output: -30→-20, -15→-10, 15→10, 30→20
- This IS a function.

Problem 11:
- Input values: -8, -3, 6, 7, 6 (note that 6 appears twice)
- The input 6 maps to both 2 and -2 (two different outputs)
- This is NOT a function (since one input has multiple outputs).

Problem 12:
- Input values: -7, -3, 2, -6, -2, 0 (all unique inputs)
- Each input maps to exactly one output: -7→2, -3→1, 2→3, -6→-2, -2→-4, 0→5
- This IS a function.

The final answer is:
- Problems 1, 2, 4, 5, 6, 7, 8, 9, 10, 12 are functions (mark with ✓)
- Problems 3 and 11 are not functions (mark with X)