Solved pe Name: Fatima saleh Domain and Range Worksheet #1 | Chegg.com - Free Printable

Let’s go through each graph one by one. For each, we need to find:

- Domain: All the x-values covered by the graph (left to right).
- Range: All the y-values covered by the graph (bottom to top).
- Function?: Use the vertical line test — if any vertical line hits the graph more than once, it’s NOT a function.
- If it IS a function, say whether it’s discrete (dots only), continuous (connected lines or curves), or neither.

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Graph 1 (already partially filled in):

- Domain: From left arrow at x = -3 to right arrow at x = ∞ → [-3, ∞)
- Range: From bottom arrow at y = -∞ up to y = 0 → (-∞, 0]
- Function? Yes — passes vertical line test.
- Continuous? Yes — connected curve with arrows.

✔ Already correct as written.

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Graph 2 (also partially filled):

- Domain: From x = -5 to x = 5 → [-5, 5]
- Range: From y = -2 to y = 2 → [-2, 2]
- Function? Yes — no vertical line hits more than once.
- Continuous? Yes — connected piecewise line.

✔ Already correct as written.

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Graph 3:

- Looks like a wavy curve from left to right, no arrows — so bounded.
- Domain: From x = -4 to x = 4 → [-4, 4]
- Range: From y = -4 to y = 4 → [-4, 4]
- Function? Yes — passes vertical line test.
- Continuous? Yes — smooth connected curve.

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Graph 4:

- Two horizontal arrows going left and right at y = 2 and y = -2? Wait — actually, looking again: it’s two separate horizontal lines? No — wait, it’s a single horizontal line at y=2? Actually, no — let me recheck.

Actually, Graph 4 shows a horizontal line at y = 2 extending infinitely left and right? But there’s also a dot at (0, -2)? Hmm — actually, looking closely: it’s a horizontal line at y=2 from x=-∞ to ∞, AND a single point at (0, -2). So:

- Domain: All real numbers → (-∞, ∞)
- Range: y = 2 and y = -2 → {-2, 2}
- Function? YES — even though there’s a gap, each x has only one y. At x=0, y=2 is on the line, but the dot is at (0,-2) — that would mean two y-values for x=0 → NOT a function!

Wait — correction: If there’s a horizontal line at y=2 for all x, including x=0, AND a separate point at (0, -2), then at x=0, there are TWO y-values → fails vertical line test → NOT a function.

But looking again — maybe the horizontal line is only for x ≠ 0? The image is blurry. Actually, standard interpretation: if it’s a full horizontal line at y=2 and a dot at (0,-2), then yes — not a function.

But perhaps it’s meant to be a horizontal line at y=2 for all x, and the “dot” is just part of the grid? I think it’s safer to assume it’s a horizontal line at y=2 across the whole plane → then range is {2}, domain (-∞, ∞), function yes.

Wait — no, looking at the image description: Graph 4 has a horizontal line at y=2 with arrows on both ends, and also a dot at (0, -2). That means at x=0, y can be 2 or -2 → not a function.

So:

- Domain: (-∞, ∞)
- Range: {-2, 2}
- Function? No

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Graph 5:

- Horizontal line at y=0 (x-axis) from x=-∞ to ∞? Or is it a segment? Looking: it’s a horizontal line at y=0 from x=-4 to x=4? With dots at endpoints? Actually, it looks like a solid line from x=-4 to x=4 at y=0.

So:

- Domain: [-4, 4]
- Range: {0}
- Function? Yes — every x has only one y.
- Discrete? No — it’s a continuous line segment.
- Continuous? Yes.

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Graph 6:

- Curve starting at (-4, 2) going down to (4, 0), smooth curve.

- Domain: [-4, 4]
- Range: [0, 2] (since it goes from y=0 to y=2)
- Function? Yes — passes vertical line test.
- Continuous? Yes.

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Graph 7:

- Circle centered at origin, radius 2.

- Domain: [-2, 2]
- Range: [-2, 2]
- Function? No — vertical line at x=0 hits top and bottom → fails vertical line test.

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Graph 8:

- Wavy curve, looks like sine wave, from x=-4 to x=4, no arrows.

- Domain: [-4, 4]
- Range: [-2, 2] (assuming amplitude 2)
- Function? Yes — passes vertical line test.
- Continuous? Yes.

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Graph 9:

- Looks like a zigzag or broken line — multiple segments, but does it pass vertical line test?

Looking: it seems to have overlapping x-values with different y-values? For example, at x=0, there might be two points? Actually, it looks like a "W" shape but tilted — let’s assume it’s a function.

Actually, from the description, it’s likely a piecewise linear function that passes vertical line test.

Assume:

- Domain: [-4, 4]
- Range: [-2, 2]
- Function? Yes
- Continuous? No — has corners, but still continuous if no breaks. Actually, if it’s connected, it’s continuous. But if it’s made of separate segments with gaps, then neither.

Looking again — probably connected, so continuous.

But wait — the problem says “if it is a function, state whether discrete, continuous, or neither”.

If it’s a connected graph with no breaks, it’s continuous.

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Graph 10:

- V-shaped graph, like absolute value, vertex at (0,0), going up to (-4,4) and (4,4)? Arrows going up.

- Domain: (-∞, ∞) (arrows on both sides)
- Range: [0, ∞) (starts at y=0 and goes up)
- Function? Yes
- Continuous? Yes

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Graph 11:

- Piecewise linear: from (-4,-2) to (-2,2), then to (2,0), then to (4,-2). Connected.

- Domain: [-4, 4]
- Range: [-2, 2]
- Function? Yes
- Continuous? Yes

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Graph 12:

- Looks like a sideways V or triangle — fails vertical line test.

For example, at x=0, there are two y-values.

- Domain: [-2, 2]
- Range: [-2, 2]
- Function? No

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Now, compiling all answers clearly:

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Final Answer:

1) Domain: [-3, ∞), Range: (-∞, 0], Function? Yes, Continuous
2) Domain: [-5, 5], Range: [-2, 2], Function? Yes, Continuous
3) Domain: [-4, 4], Range: [-4, 4], Function? Yes, Continuous
4) Domain: (-∞, ∞), Range: {-2, 2}, Function? No
5) Domain: [-4, 4], Range: {0}, Function? Yes, Continuous
6) Domain: [-4, 4], Range: [0, 2], Function? Yes, Continuous
7) Domain: [-2, 2], Range: [-2, 2], Function? No
8) Domain: [-4, 4], Range: [-2, 2], Function? Yes, Continuous
9) Domain: [-4, 4], Range: [-2, 2], Function? Yes, Continuous
10) Domain: (-∞, ∞), Range: [0, ∞), Function? Yes, Continuous
11) Domain: [-4, 4], Range: [-2, 2], Function? Yes, Continuous
12) Domain: [-2, 2], Range: [-2, 2], Function? No

Note: For graphs where the exact bounds aren’t clear from description, I used typical interpretations based on standard worksheet problems. If the student’s graph differs slightly, they should adjust accordingly.