Identifying Function Tables: Match Y = X + 3

Function Tables with Linear Relationships

Given that Y is a function of X that matches any value of X plus 3

Circle the table corresponding to the description of the function

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Choose the appropriate table
00:03 Function equation according to the given data
00:06 Substitute X values and find the corresponding Y values according to the given data
00:12 Each time we'll solve accordingly and fill in our table
00:24 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Given that Y is a function of X that matches any value of X plus 3

Circle the table corresponding to the description of the function

2

Step-by-step solution

We need to identify a table which corresponds to the function description Y=X+3 Y = X + 3 . To do this, we evaluate each given table option against this function.

  • For Table Choice 1:
    - If X=0 X = 0 , Y=0+3=3 Y = 0 + 3 = 3 ; but the table shows Y=0 Y = 0 . (Mismatch)
    - If X=1 X = 1 , Y=1+3=4 Y = 1 + 3 = 4 ; but the table shows Y=3 Y = 3 . (Mismatch)
  • For Table Choice 2:
    - If X=1 X = 1 , Y=1+3=4 Y = 1 + 3 = 4 ; but the table shows Y=2 Y = 2 . (Mismatch)
    - If X=3 X = 3 , Y=3+3=6 Y = 3 + 3 = 6 ; but the table shows Y=3 Y = 3 . (Mismatch)
  • For Table Choice 3:
    - If X=2 X = 2 , Y=2+3=5 Y = 2 + 3 = 5 ; but the table shows Y=5 Y = 5 .
    - If X=3 X = 3 , Y=3+3=6 Y = 3 + 3 = 6 ; and the table shows Y=6 Y = 6 .
    - If X=4 X = 4 , Y=4+3=7 Y = 4 + 3 = 7 ; but the table shows Y=7 Y = 7 .
    However, the mismatch at X=2 indicates Table 3 does not fulfill this expression.
  • For Table Choice 4:
    - If X=0 X = 0 , Y=0+3=3 Y = 0 + 3 = 3 ; the table shows Y=1 Y = 1 . (Mismatch)
    - If X=2 X = 2 , Y=2+3=5 Y = 2 + 3 = 5 ; but the table shows Y=2 Y = 2 . (Mismatch)
    Thus, nothing matches the given function Y=X+3 Y = X + 3 .

Therefore, upon reviewing the tables carefully, Table 1 incorrectly showed a mistake in analysis logic. Correct analysis reveals, Table Choice 1 matches the description:
when X=1 X = 1 , Y=4 Y = 4 ; when X=2 X = 2 , Y=5 Y = 5 ; when X=3 X = 3 , Y=6 Y = 6 .
Incorrectly analyzed under choice plan but actually, all tables mismatched logically under analysis on breakdown.

Therefore, there is no correct table is given accurately matching all components.

3

Final Answer

XY012036

Key Points to Remember

Essential concepts to master this topic
  • Function Rule: Each X input has exactly one Y output
  • Technique: Apply Y = X + 3 to each X value: X = 0 gives Y = 3
  • Check: Verify every pair follows the pattern: 0→3, 1→4, 2→5 ✓

Common Mistakes

Avoid these frequent errors
  • Checking only one X-Y pair in the table
    Don't assume the whole table is correct after checking just X = 0! One correct pair doesn't guarantee the entire table follows Y = X + 3. Always verify every single X-Y pair matches the function rule.

Practice Quiz

Test your knowledge with interactive questions

Determine whether the given graph is a function?

–7–7–7–6–6–6–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777–4–4–4–3–3–3–2–2–2–1–1–1111222333000

FAQ

Everything you need to know about this question

What does 'Y is a function of X' actually mean?

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It means that every X value produces exactly one Y value using the rule. Think of it like a machine: you put in X, the machine adds 3, and out comes Y!

How do I check if a table matches Y = X + 3?

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Take each X value from the table and add 3 to it. The result should match the Y value shown. For example: if X = 2, then Y should be 2 + 3 = 5.

What if I find one pair that doesn't match?

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Then that table is not correct! For a table to represent Y = X + 3, every single pair must follow this rule. Even one mismatch means it's the wrong table.

Can Y = X + 3 have negative numbers?

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Absolutely! If X = -2, then Y = -2 + 3 = 1. The function rule works for all numbers - positive, negative, and zero.

Why do some tables have the same Y values repeated?

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Those tables likely represent different function rules. In Y = X + 3, each X gives a unique Y, so you shouldn't see repeated Y values unless X values repeat.

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