Function Table Analysis: Matching X Minus 5 Relationships

Q: How do I know which table matches the function Y = X - 5?

Test every pair in each table! For each X-value, calculate X - 5 and see if it matches the given Y-value. Only one table will have all pairs correct.

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

It means Y depends on X. For every X-value you put in, there's exactly one Y-value that comes out using the rule $ Y = X - 5 $.

Q: Do I need to check every row in the table?

Yes, absolutely! Even if the first row is correct, you must verify all rows. One wrong pair means the entire table doesn't match the function.

Q: What if I get confused about which operation to use?

Read carefully! The problem says 'X minus 5', so you subtract: $ Y = X - 5 $. Don't let negative numbers confuse you - just follow the rule exactly.

Q: Can a function table have negative numbers?

Absolutely! Functions can produce any real numbers - positive, negative, or zero. In this case, since we're subtracting 5, most Y-values will be negative.

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

00:13 Each time we'll solve accordingly and fill in our table

00:27 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

Y is a function of X that matches any value of X minus 5.

Which table corresponds to the function described?

2

Step-by-step solution

To solve this problem, we'll examine each table choice using the provided function $Y = X - 5$ .

Let's break down each table:

Table 1: $\begin{aligned} &X = -1 \Rightarrow Y = -1 - 5 = -6 \\ &X = 0 \Rightarrow Y = 0 - 5 = -5 \\ &X = 1 \Rightarrow Y = 1 - 5 = -4 \end{aligned}$ . All calculated values match the table.
Table 2: $\begin{aligned} &X = 3 \Rightarrow Y = 3 - 5 = -2 \\ &X = 4 \Rightarrow Y = 4 - 5 = -1 \\ &X = 5 \Rightarrow Y = 5 - 5 = 0 \end{aligned}$ . The last $Y$ value does not match.
Table 3: $\begin{aligned} &X = 0 \Rightarrow Y = 0 - 5 = -5 \\ &X = 3 \Rightarrow Y = 3 - 5 = -2 \\ &X = 6 \Rightarrow Y = 6 - 5 = 1 \end{aligned}$ . The last $Y$ value does not match.
Table 4: $\begin{aligned} &X = 2 \Rightarrow Y = 2 - 5 = -3 \\ &X = 4 \Rightarrow Y = 4 - 5 = -1 \\ &X = 5 \Rightarrow Y = 5 - 5 = 0 \end{aligned}$ . None match based on description.

Only Table 1 accurately reflects the function $Y = X - 5$ for the given $X$ values of -1, 0, and 1.

Therefore, the correct table is Choice 1.

3

Final Answer

Key Points to Remember

Essential concepts to master this topic

Function Rule: Y equals X minus 5 for every input value
Technique: Calculate Y = -1 - 5 = -6, Y = 0 - 5 = -5
Check: Every Y value must equal its corresponding X value minus 5 ✓

Common Mistakes

Avoid these frequent errors

Adding 5 instead of subtracting 5
Don't calculate Y = X + 5 instead of Y = X - 5 = wrong positive values! This reverses the operation and gives completely incorrect Y-values. Always subtract 5 from each X-value to find the correct Y-value.

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

How do I know which table matches the function Y = X - 5?

+

Test every pair in each table! For each X-value, calculate X - 5 and see if it matches the given Y-value. Only one table will have all pairs correct.

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

+

It means Y depends on X. For every X-value you put in, there's exactly one Y-value that comes out using the rule $Y = X - 5$ .

Do I need to check every row in the table?

+

Yes, absolutely! Even if the first row is correct, you must verify all rows. One wrong pair means the entire table doesn't match the function.

What if I get confused about which operation to use?

+

Read carefully! The problem says 'X minus 5', so you subtract: $Y = X - 5$ . Don't let negative numbers confuse you - just follow the rule exactly.

Can a function table have negative numbers?

+

Absolutely! Functions can produce any real numbers - positive, negative, or zero. In this case, since we're subtracting 5, most Y-values will be negative.

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