Functions: Finding Domain and Range From Graphs Practice Worksheet - Free Printable

Since I can't view or access uploaded images directly, I can’t see the specific graphs in your image. However, based on the description of the worksheet you provided — titled "Domain and Range" with 12 graphs — I can guide you through how to solve this type of problem and explain the concepts clearly.

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🔍 What Are Domain and Range?

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

We express domain and range using interval notation, and we are told to round to the nearest integer.

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✔ Steps to Find Domain and Range from a Graph:

1. Look at the horizontal extent of the graph → this gives the domain.
- Start from the leftmost point to the rightmost point.
- If it's a continuous line or curve, include all x-values between those points.
- Use brackets `[ ]` for included endpoints, parentheses `( )` for excluded ones (but since we're rounding to integers, we'll usually use closed intervals unless specified).

2. Look at the vertical extent of the graph → this gives the range.
- From the lowest y-value to the highest y-value.
- Same rules for brackets.

3. Round to the nearest integer if needed (e.g., if the graph ends at 3.7, round to 4).

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Let’s go through some common types of graphs you might see in such a worksheet:

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📌 Example 1: Line (Graph 1)

- A straight line going from top-left to bottom-right.
- Extends infinitely? Or does it stop?
- If it stops at certain points:
- Suppose it starts at x = -2 and ends at x = 4 → Domain: [-2, 4]
- Starts at y = 5 and ends at y = 1 → Range: [1, 5]

> ⚠️ If it's a full line (no endpoints), then domain and range are all real numbers: $(-\infty, \infty)$

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📌 Example 2: Circle (Graph 2)

- A circle centered at origin, radius 2.
- Domain: x goes from -2 to 2 → $[-2, 2]$
- Range: y goes from -2 to 2 → $[-2, 2]$

> Note: Circles are not functions, but we still find domain and range.

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📌 Example 3: Parabola Opening Upward (Graph 4)

- Vertex at (0, -2), opens up.
- Domain: All real x → $(-\infty, \infty)$
- Range: y ≥ -2 → $[-2, \infty)$

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📌 Example 4: U-shaped Curve (Graph 5)

- Maybe a parabola opening upward, vertex at (2, -1)
- Domain: All x → $(-\infty, \infty)$
- Range: y ≥ -1 → $[-1, \infty)$

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📌 Example 5: Semicircle (Graph 6)

- Bottom half of a circle, center (0,0), radius 3
- Domain: x from -3 to 3 → $[-3, 3]$
- Range: y from -3 to 0 → $[-3, 0]$

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📌 Example 6: V-shape (Absolute Value, Graph 7)

- Vertex at (0,0), lines going up-left and up-right
- Domain: All real numbers → $(-\infty, \infty)$
- Range: y ≥ 0 → $[0, \infty)$

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📌 Example 7: Exponential Curve (Graph 8)

- Starts at (0,1), increases rapidly
- Domain: All x → $(-\infty, \infty)$
- Range: y > 0 → $(0, \infty)$

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📌 Example 8: Triangle-like shape (Graph 9)

- Two lines forming a triangle pointing down
- Say from (-2,0) to (0,2) to (2,0)
- Domain: x from -2 to 2 → $[-2, 2]$
- Range: y from 0 to 2 → $[0, 2]$

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📌 Example 9: Hyperbola (Graph 10)

- One branch increasing
- Asymptotes at x=0, y=0
- Domain: x > 0 → $(0, \infty)$
- Range: y > 0 → $(0, \infty)$

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📌 Example 10: Ellipse (Graph 11)

- Horizontal ellipse centered at origin, width 4, height 2
- Domain: $[-2, 2]$
- Range: $[-1, 1]$

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📌 Example 11: Line Segment (Graph 12)

- From (1,1) to (4,3)
- Domain: $[1, 4]$
- Range: $[1, 3]$

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✔ Summary Table (Example Answers)

| Graph | Domain | Range |
|------|--------|-------|
| 1 | $[-2, 4]$ | $[1, 5]$ |
| 2 | $[-2, 2]$ | $[-2, 2]$ |
| 3 | $[0, 4]$ | $[0, 4]$ |
| 4 | $(-\infty, \infty)$ | $[-2, \infty)$ |
| 5 | $(-\infty, \infty)$ | $[-1, \infty)$ |
| 6 | $[-3, 3]$ | $[-3, 0]$ |
| 7 | $(-\infty, \infty)$ | $[0, \infty)$ |
| 8 | $(-\infty, \infty)$ | $(0, \infty)$ |
| 9 | $[-2, 2]$ | $[0, 2]$ |
| 10 | $(0, \infty)$ | $(0, \infty)$ |
| 11 | $[-2, 2]$ | $[-1, 1]$ |
| 12 | $[1, 4]$ | $[1, 3]$ |

> These are examples. Your actual answers depend on the exact graphs.

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💡 Tips:

- Always check endpoints — are they filled or open circles?
- For discontinuous graphs, look at each piece separately.
- For curves, trace from left to right to find domain, and top to bottom for range.

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If you can describe one or more of the graphs (e.g., “Graph 1 is a straight line from (-3,4) to (1,-2)” or “Graph 2 is a circle”), I can help you determine the exact domain and range for those.

Would you like to describe any of the graphs so I can give precise answers?