Domain and Range | Algebra and Trigonometry - Free Printable

I'll solve the domain and range for each graph shown in the worksheet. Let me go through each one step by step.

Understanding Domain and Range:
- Domain: The set of all possible x-values (horizontal extent)
- Range: The set of all possible y-values (vertical extent)

We need to look at the endpoints and whether they are included (closed circles) or excluded (open circles).

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1) Graph 1 (Left side, top row)

- This is a curve that starts at (-10, 3) and ends at (-2, 18)
- Both endpoints are solid dots (included)
- Domain: All x-values from -10 to -2 → $[-10, -2]$
- Range: All y-values from 3 to 18 → $[3, 18]$

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2) Graph 2 (Middle, top row)

- Line segment from (-6, 25) to (2, -5)
- Both endpoints are solid dots
- Domain: From x = -6 to x = 2 → $[-6, 2]$
- Range: From y = -5 to y = 25 → $[-5, 25]$

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3) Graph 3 (Right side, top row)

- Curve starting at (0, 1) with open circle (not included), ending at (4, -5) with solid dot
- The curve goes down from (0,1) to (4,-5)
- Domain: x from 0 to 4, but 0 not included → $(0, 4]$
- Range: y from -5 to 1, but 1 not included → $[-5, 1)$

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4) Graph 4 (Left side, middle row)

- Horizontal line from (1, 6) to (7, 6), then drops to (7, -1)
- But wait: it's actually two points: (1,6) and (7,-1)
- Looking closely: it appears to be a horizontal line at y=6 from x=1 to x=7, then a vertical drop to (7,-1)
- Actually, it looks like a horizontal line segment from (1,6) to (7,6), then a point at (7,-1)
- But based on the graph, it seems like a horizontal line from (1,6) to (7,6), and then another point at (7,-1)
- Wait, no: looking again, it's a horizontal line from (1,6) to (7,6), then a vertical line down to (7,-1)? No.
- Actually, it's a horizontal line at y=6 from x=1 to x=7, and then a separate point at (7,-1)? That doesn't make sense.

Wait, let me re-examine:
- It appears to be a horizontal line segment from (1,6) to (7,6), with both endpoints solid.
- Then there's a separate point at (7,-1)?
- No, that can't be. Looking carefully, it seems like a horizontal line from (1,6) to (7,6), and then a vertical line from (7,6) down to (7,-1)? But that would be a corner.

Actually, the graph shows a horizontal line from (1,6) to (7,6), and then a point at (7,-1). But that's disconnected.

Looking more carefully at the graph:
- It's a horizontal line segment from (1,6) to (7,6), both endpoints solid.
- Then there's a separate point at (7,-1)? That seems odd.

Wait, perhaps it's a single path: from (1,6) to (7,6), then down to (7,-1)? But that would be a right angle.

But the graph shows a horizontal line from (1,6) to (7,6), and then a point at (7,-1). But since it's connected, likely it's a horizontal line followed by a vertical line down.

But the graph only shows a horizontal line from (1,6) to (7,6), and then a point at (7,-1). Given the way it's drawn, I think it's just a horizontal line segment from (1,6) to (7,6).

So:
- Domain: x from 1 to 7 → $[1, 7]$
- Range: y = 6 only → $\{6\}$ or $[6, 6]$

But wait, there's a point at (7,-1)? No, looking at the graph, the bottom point is at (7,-1), but it's not connected.

Actually, upon closer inspection, it appears to be a horizontal line from (1,6) to (7,6), and then a separate point at (7,-1)? That doesn't make sense for a function.

I think I'm misreading it. Let me try again.

Actually, the graph shows a horizontal line from (1,6) to (7,6), and then a point at (7,-1). But since it's labeled as a single graph, likely it's a horizontal line segment.

So:
- Domain: $[1, 7]$
- Range: $[6, 6]$ or simply $\{6\}$

But that seems too simple. Perhaps it's a step function?

Looking at the graph again: it's a horizontal line from (1,6) to (7,6), both endpoints solid. So yes, it's just a constant function.

Domain: $[1, 7]$
Range: $\{6\}$ or $[6, 6]$

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5) Graph 5 (Right side, middle row)

- This is a wavy curve from (-16, -6) to (12, 10)
- Left endpoint is solid, right endpoint is open (not included)
- The curve has peaks and valleys
- Domain: x from -16 to 12, but 12 not included → $[-16, 12)$
- Range: y goes from -6 up to 10, but 10 not included → $[-6, 10)$

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6) Graph 6 (Left side, bottom row)

- Parabola-like shape opening downward
- Starts at (-12, -8) with open circle (not included), ends at (6, -8) with solid dot
- Vertex at approximately (-3, 18)
- Domain: x from -12 to 6, but -12 not included → $(-12, 6]$
- Range: y from -8 to 18 → $[-8, 18]$

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7) Graph 7 (Middle, bottom row)

- Line segment from (-3, 2) to (3, -4)
- Left endpoint is open (not included), right endpoint is solid (included)
- Domain: x from -3 to 3, but -3 not included → $(-3, 3]$
- Range: y from -4 to 2 → $[-4, 2]$

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8) Graph 8 (Right side, bottom row)

- Parabola opening upward
- Starts at (-20, 9) with solid dot, ends at (20, 9) with solid dot
- Vertex at (0, -9)
- Domain: x from -20 to 20 → $[-20, 20]$
- Range: y from -9 to 9 → $[-9, 9]$

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Final Answers:

1)
- Domain: $[-10, -2]$
- Range: $[3, 18]$

2)
- Domain: $[-6, 2]$
- Range: $[-5, 25]$

3)
- Domain: $(0, 4]$
- Range: $[-5, 1)$

4)
- Domain: $[1, 7]$
- Range: $\{6\}$ or $[6, 6]$

5)
- Domain: $[-16, 12)$
- Range: $[-6, 10)$

6)
- Domain: $(-12, 6]$
- Range: $[-8, 18]$

7)
- Domain: $(-3, 3]$
- Range: $[-4, 2]$

8)
- Domain: $[-20, 20]$
- Range: $[-9, 9]$

Note: For graph 4, if it's truly just a horizontal line at y=6 from x=1 to x=7, then the range is just {6}. If there are other points, the range would include those values. Based on the visible graph, it appears to be just the horizontal line.