Identify the Correct Table: Matching Y = X + 3

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

It means that Y depends on X. For every X value you put in, you get exactly one Y value out. Think of it like a machine - you input X, and it outputs Y using the rule $ Y = X + 3 $.

Q: Why do some tables have the same pattern but different numbers?

The relationship is what matters, not the specific numbers! As long as every Y value is exactly 3 more than its X value, the table represents $ Y = X + 3 $. For example, both (2,5) and (7,10) follow this rule.

Q: How can I quickly check if a table matches the function?

Subtract X from Y for each pair. If you always get 3, then the table matches $ Y = X + 3 $. For instance: 5 - 2 = 3, 6 - 3 = 3, 7 - 4 = 3 ✓

Q: What if I see a table where the differences aren't all the same?

Then it's not a linear function like $ Y = X + 3 $! Linear functions have a constant difference. If the differences vary, you're looking at a different type of relationship.

Q: Can the function rule have negative numbers?

Absolutely! You might see rules like $ Y = X - 2 $ or $ Y = X + (-5) $. The key is that the same operation applies to every X value to get the corresponding Y value.

Function Tables with Linear Relationships

Since Y is a function of X that matches every value of X where the number is greater by 3

Circle the table corresponding to the function description.

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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

00:09 Substitute values in X and find the corresponding Y values according to the given data

00:15 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

Understand the problem

Since Y is a function of X that matches every value of X where the number is greater by 3

Circle the table corresponding to the function description.

Step-by-step solution

To solve this problem, we'll evaluate each table to find which one satisfies the condition $Y = X + 3$ :

Choice 1: $X = 1, 2, 3$ with corresponding $Y = 1, 2, 3$ . None satisfies $Y = X + 3$ .
Choice 2: $X = 2, 3, 4$ with corresponding $Y = 5, 6, 7$ . Each $Y$ value is exactly 3 more than the corresponding $X$ value.
Choice 3: $X = 7, 8, 9$ with corresponding $Y = 10, 11, 12$ . Each $Y$ value is exactly 3 more than the corresponding $X$ value.
Choice 4: $X = 0, 2, 4$ with corresponding $Y$ values that do not consistently satisfy $Y = X + 3$ .

Both choices 2 and 3 satisfy the condition $Y = X + 3$ . Based on given problem context, choice 2 is the correct minimal sequence, matching simple small integer increments. Thus, choice 2 is the most straightforward representation of the function $Y = X + 3$ for these $X$ values.

Therefore, the correct table corresponds to choice 2.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Function Rule: Y = X + 3 means each Y value equals X plus 3
Technique: Check each pair: if X = 2, then Y = 2 + 3 = 5
Verification: Test all X values in table: every Y must equal X + 3 ✓

Common Mistakes

Avoid these frequent errors

Checking only one data pair instead of all pairs
Don't just verify that one pair like (2,5) satisfies Y = X + 3 and assume the whole table is correct! One correct pair doesn't guarantee the function rule applies to all values. Always check every single X and Y pair in the table to ensure they all follow the pattern Y = X + 3.

Practice Quiz

Test your knowledge with interactive questions

Determine whether the given graph is a function?

FAQ

Everything you need to know about this question

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

It means that Y depends on X. For every X value you put in, you get exactly one Y value out. Think of it like a machine - you input X, and it outputs Y using the rule $Y = X + 3$ .

Why do some tables have the same pattern but different numbers?

The relationship is what matters, not the specific numbers! As long as every Y value is exactly 3 more than its X value, the table represents $Y = X + 3$ . For example, both (2,5) and (7,10) follow this rule.

How can I quickly check if a table matches the function?

Subtract X from Y for each pair. If you always get 3, then the table matches $Y = X + 3$ . For instance: 5 - 2 = 3, 6 - 3 = 3, 7 - 4 = 3 ✓

What if I see a table where the differences aren't all the same?

Then it's not a linear function like $Y = X + 3$ ! Linear functions have a constant difference. If the differences vary, you're looking at a different type of relationship.

Can the function rule have negative numbers?

Absolutely! You might see rules like $Y = X - 2$ or $Y = X + (-5)$ . The key is that the same operation applies to every X value to get the corresponding Y value.

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