Domain and Range Worksheets - Free Printable

Since I can't view or access uploaded images directly, I can't see the specific content of your image. However, based on the description you provided — "Domain and Range - Ordered Pairs" worksheet with problems involving finding domain and range from ordered pairs and graphs — I can help you solve typical problems like these.

Let me walk through how to solve such problems in general, and then you can apply the method to your specific worksheet.

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🔹 What are Domain and Range?

- Domain: The set of all x-values (input values) in a relation.
- Range: The set of all y-values (output values) in a relation.

For ordered pairs like (x, y), we list all unique x-values for the domain and all unique y-values for the range.

For graphs, we look at:
- All x-coordinates of points → domain
- All y-coordinates of points → range

We usually write them in set notation or interval notation, depending on the context.

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✔ Example 1: Finding Domain and Range from Ordered Pairs

Suppose one problem says:

> Find the domain and range of the relation:
> {(2, 5), (–3, 1), (4, –2), (2, 7)}

Step 1: List all x-values (domain):
2, –3, 4, 2 → Remove duplicates → {–3, 2, 4}

Step 2: List all y-values (range):
5, 1, –2, 7 → No duplicates → {–2, 1, 5, 7}

✔ Answer:
- Domain: {–3, 2, 4}
- Range: {–2, 1, 5, 7}

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✔ Example 2: From a Graph

Suppose you have a graph with points at:
- (–2, 1)
- (0, 3)
- (1, –1)
- (3, 2)

Step 1: Read x-values (domain):
–2, 0, 1, 3 → Domain = {–2, 0, 1, 3}

Step 2: Read y-values (range):
1, 3, –1, 2 → Range = {–1, 1, 2, 3}

✔ Answer:
- Domain: {–2, 0, 1, 3}
- Range: {–1, 1, 2, 3}

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📈 If the Graph Has Continuous Lines or Curves

If the graph is not just discrete points but a line or curve, then:

- Domain: All x-values where the graph exists (left to right)
- Range: All y-values where the graph exists (bottom to top)

Use interval notation.

Example: A straight line from (–1, 2) to (3, 6):

- Domain: [–1, 3]
- Range: [2, 6]

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🔍 Tips for Your Worksheet

Look at each problem carefully:

#### For Part A (Ordered Pairs):
1. Extract all x-values → domain
2. Extract all y-values → range
3. Write as sets (no duplicates, order doesn’t matter)

#### For Part B (Graphs):
1. Identify all points or intervals shown
2. Determine min and max x-values → domain
3. Determine min and max y-values → range
4. Use set notation if discrete points; interval notation if continuous

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🛠️ How to Solve Your Specific Problems

Since I can't see your image, here’s what you should do:

1. For each set of ordered pairs:
- Write down all x-values → domain
- Write down all y-values → range
- Eliminate duplicates

2. For each graph:
- Look at the x-coordinates of all points → domain
- Look at the y-coordinates of all points → range
- If it's a continuous graph (like a line), use interval notation.

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🧩 Practice Problem (Try This!)

Find the domain and range of:
{(–4, 0), (–2, 3), (1, –1), (1, 5), (3, 2)}

Solution:
- Domain: x-values = –4, –2, 1, 1, 3 → Unique: {–4, –2, 1, 3}
- Range: y-values = 0, 3, –1, 5, 2 → Unique: {–1, 0, 2, 3, 5}

✔ Domain: {–4, –2, 1, 3}
✔ Range: {–1, 0, 2, 3, 5}

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If you can describe the problems or type out the ordered pairs or describe the graphs, I can help you solve them step by step!