"Worksheet to determine if relations are functions using tables and diagrams."

Let’s go through each problem one by one.

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Problem 1:

We are given a table of x and y values:

x | y
--|--
-3 | 0
-6 | -6
6 | 4
11 | -1

To check if this is a function:
→ A function means each x-value must have only ONE y-value.
→ Look at the x-values: -3, -6, 6, 11 — all different!
→ So no x repeats → each x has exactly one y → ✔ This IS a function.

Answer for #1: Yes

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Problem 2:

Table:

x | y
--|--
-2 | 7
-2 | 3
4 | 4
7 | 7

Look at x-values: -2 appears twice!
→ First time: x = -2 → y = 7
→ Second time: x = -2 → y = 3
→ Same x gives two different y’s → ✘ NOT a function.

Answer for #2: No

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Problem 3:

Table:

x | y
--|--
3 | -2
2 | 2
2 | -3
-1 | -1

x = 2 appears twice:
→ First: y = 2
→ Second: y = -3
→ Same x, different y → ✘ NOT a function.

Answer for #3: No

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Problem 4:

Table:

x | y
--|--
10 | 7
10 | 7
20 | -3
-10 | 3

x = 10 appears twice, but both times y = 7 → same output!
→ That’s okay! Function allows same y for same x (as long as it’s not different y’s).
→ All other x’s are unique.
→ So every x has only ONE y → ✔ This IS a function.

Answer for #4: Yes

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Problem 5:

This is a mapping diagram (arrows from x to y).

Left side (x): -3, -1, 0, 2
Right side (y): 3, 2, 1, 0

Arrows:
- -3 → 3
- -1 → 2
- 0 → 1
- 2 → 0

Each x has only ONE arrow going out → each x maps to one y → ✔ This IS a function.

Answer for #5: Yes

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Problem 6:

Mapping diagram:

Left (x): -3, -1, 0, 2
Right (y): 3, 2, 1, 0

Arrows:
- -3 → 3
- -3 → 2 ← Uh oh! Two arrows from -3!
- -1 → 1
- 0 → 0
- 2 → ? (looks like maybe none? or unclear, but we already have a problem)

Since x = -3 maps to TWO different y-values (3 and 2), that breaks the rule → ✘ NOT a function.

Answer for #6: No

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Final Answers:

1. Yes
2. No
3. No
4. Yes
5. Yes
6. No

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Final Answer:
1. Yes
2. No
3. No
4. Yes
5. Yes
6. No