Function Table Analysis: Validating Input-Output Pairs (-1,5), (0,8), (1,11)

Function Definition with Unique Input Values

Determine whether the following table represents a function

XY-1015811

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Does the following table represent a function?
00:03 A function has a constant slope, a constant difference between Y values
00:07 Let's examine the differences between Y values and try to find the slope
00:10 Therefore the slope equals the difference, a graph with a slope is a function
00:13 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

Determine whether the following table represents a function

XY-1015811

2

Step-by-step solution

It is important to remember that a constant function describes a situation where as the X value increases, the function value (Y) remains constant.

In the table, we can observe that there is a constant change in X values, meaning an increase of 1, and a constant change in Y values, meaning an increase of 3

Therefore, according to the rule, the table describes a function.

3

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic
  • Function Rule: Each x-value must pair with exactly one y-value
  • Technique: Check input column: -1→5, 0→8, 1→11 (all unique)
  • Check: No repeated x-values in first row means valid function ✓

Common Mistakes

Avoid these frequent errors
  • Confusing function definition with pattern recognition
    Don't look for arithmetic patterns like +3 in y-values = missing the point! A function isn't about patterns, it's about unique inputs. Always check that each x-value appears only once in the input row.

Practice Quiz

Test your knowledge with interactive questions

Determine whether the following table represents a constant function:

XY02468-3-3-3-3-3

FAQ

Everything you need to know about this question

Does a function need to have a pattern in the y-values?

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No! Functions don't require patterns. The y-values can be any numbers as long as each x-value maps to exactly one y-value. Random outputs like (1→5), (2→100), (3→2) still make a valid function.

What if two different x-values give the same y-value?

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That's perfectly fine for functions! Multiple inputs can have the same output. For example: (1→5), (2→5), (3→7) is still a function because each x-value has only one corresponding y-value.

How do I quickly check if a table represents a function?

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Look at the x-column only! If you see any repeated x-values, it's not a function. In our table: -1, 0, 1 are all different, so it is a function.

Why does the explanation mention constant changes?

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The explanation talks about patterns, but that's extra information. The real test is unique x-values. Even if there were no pattern (like -1→5, 0→2, 1→99), it would still be a function!

What would make this table NOT a function?

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If any x-value appeared twice with different y-values, like:

  • x: -1, 0, 1, 1
  • y: 5, 8, 11, 20

Then x=1 would map to both 11 and 20, violating the function rule.

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