Domain and Range of Continuous Graphs worksheet with set notation practice.

It looks like you've uploaded a worksheet titled "Domain & Range: Continuous Graphs", which asks students to identify the domain and range of various continuous graphs using set notation. Since I can't view images directly, I’ll guide you through how to solve this type of problem step by step, assuming the worksheet contains 12 graphs (numbered 1–12), each with a line or curve plotted on a coordinate grid.

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🔍 What are Domain and Range?

- Domain: The set of all possible x-values (horizontal axis) for which the graph exists.
- Range: The set of all possible y-values (vertical axis) for which the graph exists.

For continuous graphs, we look at the leftmost to rightmost points for domain and bottommost to topmost points for range.

We express answers in set notation, often using interval notation:
- Example: $[a, b]$ means from $a$ to $b$, including both endpoints.
- $(a, b)$ means not including endpoints.
- Use $\infty$ or $-\infty$ if it extends infinitely.

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✔ Step-by-Step Guide to Solve Each Problem

Let’s assume the graphs are typical linear or piecewise continuous lines.

#### For each graph:

1. Look at the x-axis:
- Find the leftmost point → smallest x-value
- Find the rightmost point → largest x-value
- Determine if endpoints are included (closed circle = included, open circle = excluded)

2. Look at the y-axis:
- Find the lowest point → smallest y-value
- Find the highest point → largest y-value
- Check if endpoints are included

3. Write in interval notation:
- Domain: $[x_{\text{min}}, x_{\text{max}}]$, etc.
- Range: $[y_{\text{min}}, y_{\text{max}}]$, etc.

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📌 Common Examples

Let’s suppose one graph is a straight line going from point $(-3, 2)$ to $(5, 6)$, with closed circles at both ends.

- Domain: All x-values from $-3$ to $5$: $[-3, 5]$
- Range: All y-values from $2$ to $6$: $[2, 6]$

Another example: A ray starting at $(-1, 0)$ and extending upward to infinity.

- Domain: $[-1, \infty)$
- Range: $[0, \infty)$

If the graph goes infinitely in both directions (like a line with no bounds), then:
- Domain: $(-\infty, \infty)$
- Range: $(-\infty, \infty)$

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🧩 Tips for Reading the Graphs

- If the graph has arrows at the ends, it continues infinitely.
- Closed dots mean that value is included; open dots mean it's not.
- For horizontal lines, domain is all real numbers unless restricted.
- For vertical lines, domain is a single number, but such graphs are not functions.

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📝 How to Fill Out the Worksheet

For each numbered graph:

1. Examine the graph carefully.
2. Identify the leftmost and rightmost x-values → Domain.
3. Identify the lowest and highest y-values → Range.
4. Write them in interval notation.

Example answer format:
> Domain: $[1, 4]$
> Range: $[2, 6]$

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❗ Important Notes

- If a graph starts at $x=2$ and goes to infinity: Domain = $[2, \infty)$
- If it approaches but never reaches a value: use parentheses.
- Always check for discontinuities, though the title says "continuous graphs", so likely smooth lines.

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💡 Final Advice

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

1. Label the axes on each graph.
2. Find the endpoints (or arrows).
3. Determine inclusion of endpoints.
4. Use correct interval notation.
5. Double-check whether the graph is bounded or unbounded.

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If you can describe one or two of the graphs (e.g., “Graph #1 is a line from (-2, 1) to (3, 5) with closed dots”), I can help you solve those specifically.

Would you like to describe any of the graphs?