The graph represents a relation where x represents the independent variable and y represents the dependent variable.

a coordinate plane with points at negative 5 comma 1, negative 3 comma 0, 0 comma negative 3, 2 comma 3, 5 comma negative 1, and 5 comma 1

Is the relation a function? Explain.

No, because for each output there is not exactly one input
No, because for each input there is not exactly one output
Yes, because for each output there is exactly one input
Yes, because for each input there is exactly one output

To determine if the given relation is a function, we need to verify if each input \( x \) corresponds to exactly one output \( y \). This means that for each unique \( x \)-coordinate, there should be exactly one \( y \)-coordinate.

Let's examine the points provided:

1. \((-5, 1)\)
2. \((-3, 0)\)
3. \((0, -3)\)
4. \((2, 3)\)
5. \((5, -1)\)
6. \((5, 1)\)

Notice that the \( x \)-coordinate 5 has two different \( y \)-coordinates: \(-1\) and \(1\). This indicates that for the input \( x = 5 \), there are two different outputs, \(-1\) and \(1\).

Therefore, the relation is not a function because there is at least one input that corresponds to more than one output.

The correct explanation is:
No, because for each input there is not exactly one output.

Do you want details or have any questions?

Here are 5 more questions you might find interesting:
1. How do you determine the domain and range of a function?
2. What is the vertical line test, and how does it help identify functions?
3. Can a function have two different inputs with the same output?
4. What are the characteristics of a one-to-one function?
5. How do you find the inverse of a function, and when does it exist?

**Tip:** Always remember that in a function, each input must map to exactly one output. This is the key property that distinguishes functions from general relations.

Understand how to determine if a relation is a function using specific examples. This explanation covers the key concept of functions versus relations and provides a detailed analysis of input-output relationships in mathematics.

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