Function Table Selection: Identifying Y = X + 8 Relationship

Q: How do I know which table matches Y = X + 8?

Test every X-Y pair in each table! For Y = X + 8, take each X value, add 8, and see if you get the corresponding Y value. Only the correct table will have all pairs following this rule.

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

It means that for every X value, there's exactly one Y value that goes with it. The function rule (like Y = X + 8) tells you how to find that Y value from any given X.

Q: Why can't I just look at the first pair to choose the table?

Because one correct pair doesn't guarantee the whole table is right! You might get lucky with the first pair, but the other pairs could be wrong. Always check all the pairs to be sure.

Q: What if I get confused by negative numbers?

Remember: adding 8 to a negative number makes it less negative! For example, -5 + 8 = 3. Think of it as moving 8 steps to the right on a number line.

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

00:08 Substitute values in X and find the corresponding Y values according to the given data

00:16 Each time we'll solve accordingly and fill in our table

00:34 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

Since Y is a function of X that matches every value of X where the number is greater by 8

Circle the table corresponding to the function description.

2

Step-by-step solution

To solve this problem, we need to determine the table that represents the function described by the equation $Y = X + 8$ .

Let's examine each possible table choice:

Choice 1: $\begin{array}{c|c} X & Y \\ \hline -1 & 7 \\ 2 & 10 \\ 5 & 15 \end{array}$ For $X = -1$ , $Y = -1 + 8 = 7$ (correct), $X = 2$ , $Y = 2 + 8 = 10$ (correct), $X = 5$ , $Y = 5 + 8 == 13$ . This does not satisfy for $X = 5$ .
Choice 2: $\begin{array}{c|c} X & Y \\ \hline 3 & -1 \\ 8 & -8 \\ 13 & -4 \end{array}$ This choice does not satisfy any of the pairings.
Choice 3: $\begin{array}{c|c} X & Y \\ \hline -5 & 3 \\ 0 & 8 \\ 5 & 13 \end{array}$ Verify: $X = -5 \implies Y = -5 + 8 = 3$ (correct), $X = 0 \implies Y = 0 + 8 = 8$ (correct), $X = 5 \implies Y = 5 + 8 = 13$ (correct). All values satisfy $Y = X + 8$ .
Choice 4: $\begin{array}{c|c} X & Y \\ \hline 3 & 5 \\ 2 & 7 \\ 1 & 9 \end{array}$ This choice does not satisfy the equation for any pair.

Upon checking each table, Choice 3 is the only one that correctly matches the description of the function $Y = X + 8$ for all $X$ values shown.

Therefore, the solution is that the correct table is Choice 3.

3

Final Answer

Key Points to Remember

Essential concepts to master this topic

Function Rule: Y = X + 8 means add 8 to every X value
Technique: Check each pair: X = -5, Y = -5 + 8 = 3
Verification: Test all X-Y pairs in the table follow the same pattern ✓

Common Mistakes

Avoid these frequent errors

Not checking all coordinate pairs in the table
Don't just verify one X-Y pair and assume the table is correct = missing wrong pairs! One correct pair doesn't guarantee the entire table follows Y = X + 8. Always check every single coordinate pair in the table matches the function rule.

Practice Quiz

Test your knowledge with interactive questions

Is the given graph a function?

FAQ

Everything you need to know about this question

How do I know which table matches Y = X + 8?

+

Test every X-Y pair in each table! For Y = X + 8, take each X value, add 8, and see if you get the corresponding Y value. Only the correct table will have all pairs following this rule.

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

+

It means that for every X value, there's exactly one Y value that goes with it. The function rule (like Y = X + 8) tells you how to find that Y value from any given X.

Why can't I just look at the first pair to choose the table?

+

Because one correct pair doesn't guarantee the whole table is right! You might get lucky with the first pair, but the other pairs could be wrong. Always check all the pairs to be sure.

What if I get confused by negative numbers?

+

Remember: adding 8 to a negative number makes it less negative! For example, -5 + 8 = 3. Think of it as moving 8 steps to the right on a number line.

How do I verify my chosen table is correct?

+

Substitute each X value from your chosen table into Y = X + 8. If you get the corresponding Y values shown in the table for all pairs, then you've found the right answer!

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