Worksheet with six graphs to analyze for domain, range, and function status.

Let's analyze each of the six graphs one by one to determine:

1. Domain – the set of all possible input values (x-values)
2. Range – the set of all possible output values (y-values)
3. Whether it is a function (using the vertical line test)
4. Whether the graph is continuous, discrete, or neither

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Graph 1 (Top Left)

- Points shown: Isolated dots at:
- (-4, 4), (-2, 0), (-1, 2), (0, -2), (1, -4), (2, 0), (3, 4)
- These are individual points, not connected.

#### Analysis:
- Domain: x-values: {-4, -2, -1, 0, 1, 2, 3} → Discrete
- Range: y-values: {4, 0, 2, -2, -4} → Discrete
- Function? Yes — no two points share the same x-value.
- Type: Discrete

✔ Answer:
- Domain: {-4, -2, -1, 0, 1, 2, 3}
- Range: {-4, -2, 0, 2, 4}
- Function? Yes
- Type: Discrete

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Graph 2 (Top Middle)

- This is a closed shape resembling a diamond (a square rotated 45°) centered at origin.
- It has solid lines connecting points.
- The shape includes all points along the edges.

#### Analysis:
- Domain: x-values from -3 to 3 → [-3, 3]
- Range: y-values from -3 to 3 → [-3, 3]
- Function? No — vertical line test fails. For example, at x = 0, there are multiple y-values (from y = -3 to y = 3).
- Type: Continuous (it's a solid shape with no breaks)

✔ Answer:
- Domain: [-3, 3]
- Range: [-3, 3]
- Function? No
- Type: Continuous

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Graph 3 (Top Right)

- A piecewise graph made of line segments.
- Starts at open circle at (-4, 2), goes down to (-1, 0), then horizontal to (1, 0), then up to (4, 2) with an arrow indicating continuation?
- But wait: the last segment ends at (4, 2) with a filled dot, and arrow pointing up — but no further points shown. So likely just defined on this interval.
- However, note: the first point is open circle at (-4, 2), so x = -4 is not included.

#### Points:
- Open at (-4, 2): not included
- Then line to (-1, 0), then flat to (1, 0), then up to (4, 2)

So:
- Domain: x from -4 (not included) to 4 (included) → (-4, 4]
- Range: y-values from 0 to 2 → [0, 2]
- Function? Yes — every x has only one y.
- Type: Continuous (connected line segments, no jumps)

✔ Answer:
- Domain: (-4, 4]
- Range: [0, 2]
- Function? Yes
- Type: Continuous

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Graph 4 (Bottom Left)

- A circle centered at (0, 0), radius 2.
- Equation: $ x^2 + y^2 = 4 $

#### Analysis:
- Domain: x from -2 to 2 → [-2, 2]
- Range: y from -2 to 2 → [-2, 2]
- Function? No — vertical line test fails (e.g., at x=0, two y-values: 2 and -2)
- Type: Continuous (no breaks in the circle)

✔ Answer:
- Domain: [-2, 2]
- Range: [-2, 2]
- Function? No
- Type: Continuous

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Graph 5 (Bottom Middle)

- A straight line with arrows at both ends, meaning it extends infinitely.
- Passes through points like (-3, -3), (0, 0), (3, 3), etc.
- Slope = 1, y = x

#### Analysis:
- Domain: All real numbers → $(-\infty, \infty)$
- Range: All real numbers → $(-\infty, \infty)$
- Function? Yes — passes vertical line test.
- Type: Continuous

✔ Answer:
- Domain: $(-\infty, \infty)$
- Range: $(-\infty, \infty)$
- Function? Yes
- Type: Continuous

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Graph 6 (Bottom Right)

- V-shaped graph, vertex at (0, -3)
- Two lines: left side from (-3, 0) to (0, -3), right side from (0, -3) to (3, 0)
- Arrows at both ends → extends infinitely?
- Wait: the arrows are at the ends of the lines, but they're drawn only between x = -3 and x = 3?

Actually, looking closely:
- The graph shows two rays: from (-3, 0) to (0, -3), then (0, -3) to (3, 0), and arrows at both ends.
- But that would imply it continues beyond x = ±3.

Wait — the arrows are at the endpoints of the segments, suggesting the graph does not extend beyond x = -3 and x = 3.

But typically, if there’s an arrow, it means it continues.

Let’s check:
- Left ray: starts at (-3, 0), goes down to (0, -3), then continues to the right?
- But no — the graph shows a V-shape with vertex at (0, -3), and lines going from (-3, 0) to (0, -3), and (0, -3) to (3, 0). And arrows at the ends of these segments — i.e., at (-3,0) and (3,0).

That suggests it's only defined from x = -3 to x = 3, with filled dots at endpoints.

So:
- Domain: [-3, 3]
- Range: From minimum y = -3 to maximum y = 0 → [-3, 0]
- Function? Yes — passes vertical line test.
- Type: Continuous (connected lines, no gaps)

✔ Answer:
- Domain: [-3, 3]
- Range: [-3, 0]
- Function? Yes
- Type: Continuous

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Final Answers Summary:

| Graph | Domain | Range | Function? | Type |
|-------|--------|--------|-----------|------|
| 1 | {-4, -2, -1, 0, 1, 2, 3} | {-4, -2, 0, 2, 4} | Yes | Discrete |
| 2 | [-3, 3] | [-3, 3] | No | Continuous |
| 3 | (-4, 4] | [0, 2] | Yes | Continuous |
| 4 | [-2, 2] | [-2, 2] | No | Continuous |
| 5 | $(-\infty, \infty)$ | $(-\infty, \infty)$ | Yes | Continuous |
| 6 | [-3, 3] | [-3, 0] | Yes | Continuous |

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Notes:

- Discrete: Only isolated points.
- Continuous: Connected with no breaks.
- Function: Every x has exactly one y (vertical line test).
- Graph 2 and 4 are not functions due to multiple outputs for some inputs.

Let me know if you want the answers formatted for filling in the blanks!