Determine Functionality: Evaluating the Table from X = -2 to X = 14

Q: Can two different X-values have the same Y-value?

Yes! Multiple inputs can produce the same output. For example, both $X = 3$ and $X = 5$ could map to $Y = 7$ and it's still a function.

Q: What if an X-value appears twice with different Y-values?

Then it's not a function! Each input must have exactly one output. If $X = 2$ maps to both $Y = 5$ and $Y = 8$, the relation fails the function test.

Q: How do I read the table correctly?

The top row shows input values (X) and the bottom row shows output values (Y). Each column represents one ordered pair $(X, Y)$.

Q: Do all the X-values need to follow a pattern?

No! The X-values can be any numbers in any order. What matters is that each X appears only once with its corresponding Y-value.

Q: Is this different from the vertical line test?

The vertical line test works for graphs, but for tables, just check that each input appears only once. Both methods test the same function definition!

Function Definition with Input-Output Tables

Determine whether the following table represents a function

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:12 Let's figure out if this table shows a function.

00:17 A function means each X value has only one matching Y value.

00:22 Notice that the difference between the Y values is the same.

00:27 This constant difference means the graph has a steady slope, so it's a function.

00:32 And that's how we know the answer to our question!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Determine whether the following table represents a function

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the given pairs of $(X, Y)$ .
Step 2: Verify that each $X$ maps to exactly one $Y$ .
Step 3: Conclude whether the table represents a function.

Now, let's work through each step:
Step 1: The pairs given are: $(-2, 1)$ , $(2, 6)$ , $(6, 11)$ , $(10, 16)$ , $(14, 21)$ .

Step 2: For each input value $X$ , we check its corresponding output $Y$ :

$X = -2$ maps to $Y = 1$
$X = 2$ maps to $Y = 6$
$X = 6$ maps to $Y = 11$
$X = 10$ maps to $Y = 16$
$X = 14$ maps to $Y = 21$

None of the values of

X

is associated with more than one different

Y

value.

Step 3: Since each $X$ value has exactly one corresponding $Y$ value, the table represents a function.

Yes

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic

Rule: Each input value must map to exactly one output value
Technique: Check if $X = -2$ maps only to $Y = 1$ , not multiple outputs
Check: Verify no input appears twice with different outputs ✓

Common Mistakes

Avoid these frequent errors

Focusing on whether outputs repeat instead of inputs
Don't worry if Y-values repeat like (1,3) and (2,3) = still a function! Multiple inputs can share the same output. Always check that each X-value appears only once in the table.

Practice Quiz

Test your knowledge with interactive questions

Determine whether the following table represents a constant function:

FAQ

Everything you need to know about this question

Can two different X-values have the same Y-value?

Yes! Multiple inputs can produce the same output. For example, both $X = 3$ and $X = 5$ could map to $Y = 7$ and it's still a function.

What if an X-value appears twice with different Y-values?

Then it's not a function! Each input must have exactly one output. If $X = 2$ maps to both $Y = 5$ and $Y = 8$ , the relation fails the function test.

How do I read the table correctly?

The top row shows input values (X) and the bottom row shows output values (Y). Each column represents one ordered pair $(X, Y)$ .

Do all the X-values need to follow a pattern?

No! The X-values can be any numbers in any order. What matters is that each X appears only once with its corresponding Y-value.

Is this different from the vertical line test?

The vertical line test works for graphs, but for tables, just check that each input appears only once. Both methods test the same function definition!

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