Evaluating and Identifying Functions Worksheet by Free to Discover - Free Printable

Based on my analysis of the image, I can now provide a complete solution to identify which relations are functions.

A relation is a function if and only if each input (x-value) corresponds to exactly one output (y-value).

Top Row:
1. Table 1: x=2, y=4; x=3, y=5; x=1, y=0; x=2, y=5
- x=2 appears twice with different y-values (4 and 5).
- Not a function

2. Table 2: x=2, y=4; x=3, y=6; x=4, y=8; x=5, y=10
- Each x-value appears only once.
- Function

3. Table 3: x=2, y=4; x=3, y=7; x=2, y=0; x=1, y=9
- x=2 appears twice with different y-values (4 and 0).
- Not a function

4. Graph 1: Points at (-2, 2), (0, 0), (2, -2), (4, 4)
- Each x-value has only one corresponding y-value.
- Function

5. Graph 2: Points at (-2, 2), (0, 0), (2, 2), (4, 4)
- Each x-value has only one corresponding y-value.
- Function

Bottom Row:
1. Set 1: {(0, 8), (4, 5), (5, 5)}
- Each x-value (0, 4, 5) appears only once.
- Function

2. Set 2: {(-1, 5), (2, 1), (3, 4), (5, 10)}
- Each x-value (-1, 2, 3, 5) appears only once.
- Function

3. Set 3: {(1, 8), (2, 3), (3, 10)}
- Each x-value (1, 2, 3) appears only once.
- Function

4. Mapping diagram 1: Domain {2, 4, 5}, Range {3, 7}
- 2 maps to 3, 4 maps to 7, 5 maps to 7
- Each element in the domain maps to exactly one element in the range.
- Function

5. Mapping diagram 2: Domain {2, 3, 4}, Range {5, 6, 7}
- 2 maps to 5, 3 maps to 5, 4 maps to 7
- Each element in the domain maps to exactly one element in the range.
- Function

Wait, I need to correct my analysis based on the actual image content. Let me re-examine the bottom row more carefully.

Looking at the bottom row again, I see three tables and one graph:

1. Table 1: x=1, y=0; x=3, y=5; x=5, y=2; x=8, y=0
- Each x-value appears only once.
- Function

2. Table 2: x=4, y=1; x=4, y=5; x=5, y=4; x=7, y=2
- x=4 appears twice with different y-values (1 and 5).
- Not a function

3. Table 3: x=1, y=5; x=2, y=-2; x=1, y=0; x=-3, y=-1
- x=1 appears twice with different y-values (5 and 0).
- Not a function

4. Graph: Points at approximately (-2, 2), (0, 0), (2, 2), (4, 4)
- Each x-value has only one corresponding y-value.
- Function

Actually, looking at the original image again, I realize there are two identical worksheets shown. The top worksheet has the tables, sets, and mapping diagrams I initially analyzed, while the bottom worksheet has different tables and a graph.

Let me provide the final answer based on the top worksheet, which appears to be the main focus:

Functions:
- Table 2 (top row): x=2, y=4; x=3, y=6; x=4, y=8; x=5, y=10
- Graph 1 (top right): Points at (-2, 2), (0, 0), (2, -2), (4, 4)
- Graph 2 (top right): Points at (-2, 2), (0, 0), (2, 2), (4, 4)
- Set 1: {(0, 8), (4, 5), (5, 5)}
- Set 2: {(-1, 5), (2, 1), (3, 4), (5, 10)}
- Set 3: {(1, 8), (2, 3), (3, 10)}
- Mapping diagram 1: 2→3, 4→7, 5→7
- Mapping diagram 2: 2→5, 3→5, 4→7

Not Functions:
- Table 1 (top row): x=2, y=4; x=3, y=5; x=1, y=0; x=2, y=5 (x=2 repeated with different y-values)
- Table 3 (top row): x=2, y=4; x=3, y=7; x=2, y=0; x=1, y=9 (x=2 repeated with different y-values)

The key principle is that for a relation to be a function, each input (x-value) must correspond to exactly one output (y-value). If any x-value appears more than once with different y-values, it's not a function.