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The table provides pairs of values for \( x \) and \( y \), and the task is to determine whether this represents a function.

A relation is a function if for each input \( x \), there is exactly one output \( y \). In other words, no two different pairs can have the same \( x \) value with different \( y \) values.

Let's examine the table:

\[
\begin{array}{|c|c|c|c|c|c|c|}
\hline
x & -5 & -4 & 0 & 3 & 4 & 5 \\
\hline
y & -2 & 1 & 4 & -7 & 1 & 3 \\
\hline
\end{array}
\]

- Each \( x \) value is unique: \( -5, -4, 0, 3, 4, 5 \).
- There are no repeated \( x \)-values, so each \( x \) corresponds to exactly one \( y \).

Thus, this relationship **does** represent a function.

Would you like further details or have any questions?

Here are 5 related questions:
1. What is the definition of a function?
2. Can a function have the same \( y \)-value for different \( x \)-values?
3. What would happen if an \( x \)-value appeared twice with different \( y \)-values?
4. How can you graphically represent a function from a table like this?
5. Are there types of functions where multiple outputs for one input are allowed?

**Tip:** A quick way to verify if a relation is a function is by checking for repeated \( x \)-values. If they exist, the relation is not a function.

Tell whether the relationship in this table represents a function.

Learn how to determine if a relationship in a table represents a function. This example uses pairs of x and y values and follows the basic definition of a function to verify if each input corresponds to exactly one output. Suitable for students in Grades 7-8.

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