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

Let's go through each graph on the worksheet and determine:

1. Domain – all possible x-values (horizontal extent of the graph)
2. Range – all possible y-values (vertical extent of the graph)
3. Function? – Use the Vertical Line Test: If any vertical line intersects the graph more than once, it’s not a function.
4. Discrete, Continuous, or Neither?
- Discrete: Points are separate and not connected (like dots).
- Continuous: A smooth unbroken curve or line.
- Neither: Some mix or broken pattern.

We’ll analyze each graph one by one.

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1) Graph: Vertical line at x = 0

- Domain: Only x = 0 → $ \{0\} $
- Range: From y = -3 to y = 3 → $ [-3, 3] $
- Function? Yes — only one output per input (only one point for x=0)
- Type: Discrete (single vertical line with points)

✔ Answer:
Domain: $ \{0\} $
Range: $ [-3, 3] $
Function? Yes
Type: Discrete

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2) Graph: Zig-zag line from (-5,-5) to (5,5), with sharp turns

- Domain: From x = -5 to x = 5 → $ [-5, 5] $
- Range: From y = -5 to y = 5 → $ [-5, 5] $
- Function? Yes — passes vertical line test (no vertical line hits more than once)
- Type: Continuous (connected lines)

✔ Answer:
Domain: $ [-5, 5] $
Range: $ [-5, 5] $
Function? Yes
Type: Continuous

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3) Graph: Wave-like curve (sinusoidal shape)

- Domain: From x = -3 to x = 3 → $ [-3, 3] $
- Range: From y = -2 to y = 2 → $ [-2, 2] $
- Function? Yes — every x has one y
- Type: Continuous

✔ Answer:
Domain: $ [-3, 3] $
Range: $ [-2, 2] $
Function? Yes
Type: Continuous

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4) Graph: Horizontal line segment from (-2, 2) to (2, 2)

- Domain: x goes from -2 to 2 → $ [-2, 2] $
- Range: y is always 2 → $ \{2\} $
- Function? Yes — one y-value for all x
- Type: Continuous (line segment)

✔ Answer:
Domain: $ [-2, 2] $
Range: $ \{2\} $
Function? Yes
Type: Continuous

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5) Graph: Two disconnected horizontal segments

- Top segment: from (-2, 3) to (2, 3)
- Bottom segment: from (-2, -3) to (2, -3)
- So two horizontal lines at y = 3 and y = -3, both from x = -2 to x = 2
- Domain: $ [-2, 2] $
- Range: $ \{-3, 3\} $
- Function? No — for example, at x = 0, there are two outputs: y = 3 and y = -3 → fails vertical line test
- Type: Discrete (two separate lines, but still connected horizontally)

Wait: The lines are continuous in x, but multiple y-values → not a function.

✔ Answer:
Domain: $ [-2, 2] $
Range: $ \{-3, 3\} $
Function? No
Type: Discrete (since it's made of distinct horizontal lines, though they’re continuous within themselves)

> Note: "Discrete" here refers to the set of points being disconnected vertically. Even if each piece is continuous, the overall relation is not a function.

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6) Graph: Curve starting at (-4, 4), going down to (0, 0), then continuing to (4, -4)

Looks like a downward-opening parabola or a cubic?

Actually, it looks like a cubic-like or parabola, but let's see:
- Starts at (-4, 4), goes down through origin, ends at (4, -4)
- Smooth curve

- Domain: $ [-4, 4] $
- Range: $ [-4, 4] $
- Function? Yes — passes vertical line test
- Type: Continuous

✔ Answer:
Domain: $ [-4, 4] $
Range: $ [-4, 4] $
Function? Yes
Type: Continuous

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7) Graph: Circle centered at origin, radius 2

- Equation: $ x^2 + y^2 = 4 $
- Domain: $ [-2, 2] $
- Range: $ [-2, 2] $
- Function? No — vertical line at x=0 hits two points (top and bottom)
- Type: Neither (continuous curve, but not a function; also not discrete)

But since it's a full circle, it's continuous in form, but not a function.

✔ Answer:
Domain: $ [-2, 2] $
Range: $ [-2, 2] $
Function? No
Type: Neither (it's continuous as a curve, but not a function)

> Note: "Neither" is used when it's not discrete nor continuous as a function. But technically, the graph is continuous. However, since it's not a function and not discrete, we say neither.

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8) Graph: W-shaped curve, symmetric, from x=-3 to x=3

- Looks like a quartic (degree 4) polynomial
- Peaks at (-2, 3), (0, -3), (2, 3)
- Domain: $ [-3, 3] $
- Range: $ [-3, 3] $
- Function? Yes — passes vertical line test
- Type: Continuous

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

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9) Graph: Set of points forming a "V" shape, but mirrored

- Points: (0,0), (1,1), (2,2), (3,3), (0,-1), (1,-2), (2,-3), (3,-4)
- Wait, actually: it's a V-shape pointing up and down?
- Actually, it looks like two lines: one from (0,0) to (3,3), and another from (0,0) to (3,-3)? No.
- Looking at it: seems like a "X" shape? But not quite.

Wait — it's a diagonal line from (0,0) to (3,3), and another from (0,0) to (3,-3), so it forms an "X" at origin?

But no — looking carefully: it's a single line from (0,0) to (3,3), and another from (0,0) to (3,-3)? But that would be two rays.

But the graph shows points: (0,0), (1,1), (2,2), (3,3), and (1,-1), (2,-2), (3,-3)

So two lines: one increasing, one decreasing, both passing through origin.

So:
- Domain: $ [0, 3] $
- Range: $ [-3, 3] $
- Function? No — at x=1, y=1 and y=-1 → two outputs → fails vertical line test
- Type: Discrete (dots, not connected)

✔ Answer:
Domain: $ [0, 3] $
Range: $ [-3, 3] $
Function? No
Type: Discrete

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10) Graph: V-shaped graph, vertex at (0,-2), arms going up to (-2,0) and (2,0)

- Looks like absolute value: $ y = |x| - 2 $
- Domain: $ [-2, 2] $
- Range: $ [-2, 0] $
- Function? Yes — one y per x
- Type: Continuous

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

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11) Graph: Piecewise linear, from (-3,-3) to (0,0), then to (3,-3)

- First part: line from (-3,-3) to (0,0)
- Second part: line from (0,0) to (3,-3)
- Domain: $ [-3, 3] $
- Range: $ [-3, 0] $
- Function? Yes — passes vertical line test
- Type: Continuous

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

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12) Graph: Two lines crossing, forming an "X"

- One line from (-2,2) to (2,-2)
- Another from (-2,-2) to (2,2)
- So two diagonals: one positive slope, one negative
- Domain: $ [-2, 2] $
- Range: $ [-2, 2] $
- Function? No — at x=0, both lines pass through (0,0) — wait, same point? But actually, both lines pass through origin, so at x=0, y=0 only? Wait no.

Wait: first line: from (-2,2) to (2,-2): y = -x
Second line: from (-2,-2) to (2,2): y = x

At x=0, both give y=0 → only one point. But what about other x?

At x=1: y = -1 and y = 1 → two different y-values → fails vertical line test

So not a function

- Type: Discrete? No — lines are continuous, but it's a combination. Since it's drawn as continuous lines, but not a function → Neither

But typically, such graphs are considered continuous in shape, but since it's not a function, and not discrete, we say Neither

✔ Answer:
Domain: $ [-2, 2] $
Range: $ [-2, 2] $
Function? No
Type: Neither

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✔ Final Answers:

| # | Domain | Range | Function? | Type |
|---|---------------|---------------|-----------|------------|
| 1 | {0} | [-3, 3] | Yes | Discrete |
| 2 | [-5, 5] | [-5, 5] | Yes | Continuous |
| 3 | [-3, 3] | [-2, 2] | Yes | Continuous |
| 4 | [-2, 2] | {2} | Yes | Continuous |
| 5 | [-2, 2] | {-3, 3} | No | Discrete |
| 6 | [-4, 4] | [-4, 4] | Yes | Continuous |
| 7 | [-2, 2] | [-2, 2] | No | Neither |
| 8 | [-3, 3] | [-3, 3] | Yes | Continuous |
| 9 | [0, 3] | [-3, 3] | No | Discrete |
|10 | [-2, 2] | [-2, 0] | Yes | Continuous |
|11 | [-3, 3] | [-3, 0] | Yes | Continuous |
|12 | [-2, 2] | [-2, 2] | No | Neither |

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🔍 Notes:

- Discrete: Graphs made of isolated points or separate segments.
- Continuous: Unbroken curves or lines.
- Neither: When it's not discrete (has connected parts) but not a function, or mixed.

Let me know if you'd like this formatted for printing or want explanations for specific ones!