what is the domain of the relation graphed below

Guri Bee

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19-10-2024

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Understanding the Domain of a Relation: A Visual Guide

The domain of a relation is the set of all possible input values, often represented by the x-axis on a graph. Let's explore how to determine the domain of a relation by looking at its graph.

What is a Relation?

A relation is simply a set of ordered pairs, where each pair represents a connection between two values. It's helpful to think of a relation as a set of instructions that link one value (input) to another (output).

Visualizing the Domain

When looking at a graph, the domain is the set of all x-values that have a corresponding y-value. Here's a visual explanation:

• Imagine a vertical line sweeping across the graph.
• The x-values where the line intersects the graph represent points within the domain.

Example:

Let's consider a simple example:

• Sweeping a vertical line across the graph, we see that the line intersects the graph for every possible x-value.
• Therefore, the domain of this relation is all real numbers.

Example with a Specific Restriction:

Now, let's look at an example where the domain is restricted:

• The vertical line intersects the graph for all x-values between -2 and 2 (inclusive).
• The domain of this relation is all real numbers between -2 and 2, including -2 and 2.

Important Considerations:

• Holes in the graph: If there is a hole in the graph at a specific x-value, that x-value is not included in the domain.
• Vertical asymptotes: If there is a vertical asymptote at a specific x-value, that x-value is not included in the domain.
• Domain vs. Range: While we've focused on the domain (x-values), the range represents the set of all possible output values (y-values). To determine the range, we'd sweep a horizontal line across the graph instead.

Key Takeaways:

• The domain of a relation represents all possible input values.
• Visualizing the domain on a graph involves sweeping a vertical line across the graph.
• Be aware of holes, vertical asymptotes, and other graph features that might restrict the domain.

Additional Resources:

• Khan Academy: Domain and Range
• Math is Fun: Domain and Range

Note: This article provides a basic overview of understanding the domain of a relation from a graph. For a more in-depth understanding, consult the provided resources or your textbook.