Domain and Range of a Function Worksheets - Free Printable

It looks like you've uploaded an image containing a worksheet titled "Domain and Range" with the instruction: *"Find the domain and range for each graph."* The worksheet includes eight graphs, each plotted on a coordinate plane, and you're being asked to determine the domain (all possible x-values) and range (all possible y-values) for each.

Since I can't view images directly, I’ll guide you through how to solve this type of problem step by step. If you can describe the graphs or provide details about them (e.g., whether they are lines, parabolas, discrete points, etc.), I can help you find the domain and range for each.

But here’s a general method:

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🔍 How to Find Domain and Range from a Graph

#### ✔ Domain:
The set of all x-values (horizontal extent) that the graph covers.
- Look left to right: what is the smallest and largest x-value shown?
- If the graph extends infinitely in either direction, use infinity (±∞).
- For discrete points, list the x-values.
- Use interval notation (e.g., [−3, 5]) or set notation.

#### ✔ Range:
The set of all y-values (vertical extent) that the graph covers.
- Look up and down: what is the smallest and largest y-value?
- Same rules apply as above.

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📌 Common Graph Types & Their Domains/Ranges

| Graph Type | Example | Domain | Range |
|-----------|--------|--------|-------|
| Straight line (no restrictions) | y = x | All real numbers: $(-\infty, \infty)$ | $(-\infty, \infty)$ |
| Parabola opening up | y = x² | $(-\infty, \infty)$ | $[0, \infty)$ |
| Parabola opening down | y = -x² | $(-\infty, \infty)$ | $(-\infty, 0]$ |
| Vertical line | x = 2 | {2} (only one x-value) | $(-\infty, \infty)$ |
| Horizontal line | y = 3 | $(-\infty, \infty)$ | {3} |
| Discrete points | e.g., (1,2), (3,4) | {1, 3} | {2, 4} |
| Ray or half-line | Starting at (0,0) going up-right | $[0, \infty)$ | $[0, \infty)$ |

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🧩 Steps to Solve Each Graph

For each of the 8 graphs on your worksheet:

1. Look at the x-axis:
- Is the graph defined from left to right?
- Does it start/stop at certain points?

2. Look at the y-axis:
- What's the lowest and highest point?

3. Check for endpoints:
- Are they filled circles (included)? Or open circles (not included)?
→ Use brackets `[ ]` for included, parentheses `( )` for excluded.

4. Write answer in interval notation.

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❓ Example:

Suppose one graph shows a line segment from (-2, 1) to (3, 4), with both endpoints filled.

- Domain: From x = -2 to x = 3 → $[-2, 3]$
- Range: From y = 1 to y = 4 → $[1, 4]$

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📝 Final Advice:

If you can describe each graph (e.g., "Graph A is a line from (-3,0) to (3,6)", or "Graph B is a parabola opening downward with vertex at (0,5)"), I can give you the exact domain and range for each.

Let me know how you'd like to proceed!