Domain and Range Worksheet for 9th - 11th Grade | Lesson Planet - Free Printable

Since I can't view or access uploaded images directly, I can't see the specific graphs or functions in your image. However, based on your description and the typical format of such worksheets, I can guide you through how to determine the domain and range for each function shown in a graph.

Let me walk you through the general method, and then you can apply it to each graph:

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🔹 What is Domain and Range?

- Domain: The set of all possible x-values (inputs) for which the function is defined.
- Range: The set of all possible y-values (outputs) that the function can produce.

You determine these by looking at the graph:
- Domain: Look left to right — what x-values are covered?
- Range: Look bottom to top — what y-values are covered?

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🔹 How to Find Domain & Range from a Graph

1. Look at the horizontal extent (left to right) → this gives the domain.
2. Look at the vertical extent (bottom to top) → this gives the range.
3. Use interval notation to write your answer.
- Use parentheses `()` for open endpoints (not included).
- Use brackets `[]` for closed endpoints (included).
- Use ∞ or -∞ for unbounded ends.

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🔹 Let’s Apply This to Common Graph Types

Here are some examples based on typical graphs found on such worksheets:

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#### ✔ Graph 1: Cubic Function (like \( f(x) = x^3 \))
- Graph shape: Curve going from bottom-left to top-right, passing through origin.
- Domain: All real numbers → \( (-\infty, \infty) \)
- Range: All real numbers → \( (-\infty, \infty) \)

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#### ✔ Graph 2: Parabola opening upward (like \( f(x) = x^2 \))
- Vertex at bottom, opens up.
- Domain: All real numbers → \( (-\infty, \infty) \)
- Range: From vertex y-value upward → e.g., if vertex is at (0,0), then \( [0, \infty) \)

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#### ✔ Graph 3: S-shaped curve (like a cubic with inflection point)
- Domain: Usually all real numbers unless restricted → \( (-\infty, \infty) \)
- Range: Check lowest and highest points → if it goes from bottom to top continuously, likely \( (-\infty, \infty) \)

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#### ✔ Graph 4: Rational Function (like \( f(x) = \frac{1}{x} \))
- Vertical asymptote at x = 0, two branches.
- Domain: All x except where undefined → \( (-\infty, 0) \cup (0, \infty) \)
- Range: All y except y = 0 → \( (-\infty, 0) \cup (0, \infty) \)

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#### ✔ Graph 5: Absolute Value Function (like \( f(x) = |x| \))
- V-shape, vertex at origin.
- Domain: All real numbers → \( (-\infty, \infty) \)
- Range: From vertex y-value up → \( [0, \infty) \)

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#### ✔ Graph 6: Square Root Function (like \( f(x) = \sqrt{x} \))
- Starts at (0,0), increases slowly.
- Domain: x ≥ 0 → \( [0, \infty) \)
- Range: y ≥ 0 → \( [0, \infty) \)

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📌 Tips:

- If there's a hole in the graph, exclude that x-value from domain.
- If there's an asymptote, check if values approach but never reach.
- If the graph has endpoints, use brackets; if it continues infinitely, use infinity symbols.

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❗️To Help You Better:

Please describe each graph or tell me:
- The shape of the graph
- Any key points (like vertex, intercepts, asymptotes)
- Or list the functions if they're labeled

Then I can give exact domain and range answers for each one.

Alternatively, if you can type out the functions or describe the graphs, I’ll solve them step-by-step!