Relations and Functions - Free Printable

To determine if a mapping diagram represents a function, we need to check one specific rule: Every input (number in the left oval) must have exactly one output (number in the right oval).

- If an input has no line coming from it, it is Not a Function.
- If an input has two or more lines coming from it (pointing to different outputs), it is Not a Function.
- If every input has exactly one line coming from it, it is a Function. (It is okay for multiple inputs to point to the same output).

Let's look at each problem step-by-step:

1)
- Input 0 goes to 8.
- Input 1 goes to 5.
- Input 2 goes to 6.
- Input 5 goes to 7.
- Input 6 goes to 8.
- Every number on the left has exactly one line.
- Result: Function

2)
- Look at input 6. It has two lines coming out of it (one goes to 4, one goes to 6).
- Because one input has two outputs, this fails the rule.
- Result: Not Function

3)
- Input 2 goes to 5.
- Input 8 goes to 5.
- Input 9 goes to 5.
- Even though they all go to the same number, each input on the left has only *one* line. This is allowed.
- Result: Function

4)
- Look at input 9. It has two lines coming out of it (one goes to 2, one goes to 6).
- Because one input has two outputs, this fails the rule.
- Result: Not Function

5)
- Input 1 goes to 7.
- Input 2 goes to 3.
- Input 4 goes to 2.
- Input 5 goes to 9.
- Input 9 goes to 3.
- Every number on the left has exactly one line.
- Result: Function

6)
- Look at input 0. It has two lines coming out of it (one goes to 2, one goes to 6).
- Because one input has two outputs, this fails the rule.
- Result: Not Function

7)
- Input 1 goes to 4.
- Input 2 goes to 8.
- Input 8 goes to 9.
- Every number on the left has exactly one line.
- Result: Function

8)
- Look at input 0. It has two lines coming out of it (one goes to 3, one goes to 6... wait, looking closer at diagram 8).
- Let's re-examine diagram 8 carefully.
- Input 0 connects to 3.
- Input 2 connects to 3.
- Input 4 connects to 9.
- Input 7 connects to 6.
- Wait, let me look really closely at the lines in #8.
- Line from 0 goes to 3.
- Line from 2 goes to 3.
- Line from 4 goes to 9.
- Line from 7 goes to 6.
- Each input (0, 2, 4, 7) has exactly one line starting from it.
- Therefore, this IS a function. Multiple inputs can go to the same output (0 and 2 both go to 3), but no single input splits into two paths.
- Result: Function

Let me double-check #8 again just to be sure I didn't misread the crossing lines.
- Left side: 0, 2, 4, 7.
- Right side: 3, 6, 9.
- Line 1: Starts at 0, ends at 3.
- Line 2: Starts at 2, ends at 3.
- Line 3: Starts at 4, ends at 9.
- Line 4: Starts at 7, ends at 6.
- Yes, every input has exactly one output. It is a function.

Final Answer:
1) Function
2) Not Function
3) Function
4) Not Function
5) Function
6) Not Function
7) Function
8) Function