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

Let's go through each graph one by one and determine:

1. Domain – the set of all possible x-values (horizontal extent).
2. Range – the set of all possible y-values (vertical extent).
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.
- Continuous: Graph is connected with no breaks.
- Neither: A mix or undefined.

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1)

- Graph: A straight line passing through origin, going up to the right.
- 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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2)

- Graph: A zigzag line from $x = -5$ to $x = 5$, with sharp turns.
- Domain: $[-5, 5]$
- Range: From lowest point $y = -2$ to highest $y = 4$ → $[-2, 4]$
- Function? Yes (each x has only one y)
- Type: Continuous (connected line)

✔ Answer:
Domain: $[-5, 5]$
Range: $[-2, 4]$
Function? Yes
Type: Continuous

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3)

- Graph: A sine-like wave from $x = -3$ to $x = 3$, peaks at $y = 3$, dips to $y = -3$
- 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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4)

- Graph: A single point at $(0, 0)$
- Domain: $\{0\}$
- Range: $\{0\}$
- Function? Yes (only one input, one output)
- Type: Discrete

✔ Answer:
Domain: $\{0\}$
Range: $\{0\}$
Function? Yes
Type: Discrete

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5)

- Graph: A horizontal line segment from $x = -3$ to $x = 3$, at $y = 1$
- Domain: $[-3, 3]$
- Range: $\{1\}$
- Function? Yes (every x maps to same y)
- Type: Continuous (solid line)

✔ Answer:
Domain: $[-3, 3]$
Range: $\{1\}$
Function? Yes
Type: Continuous

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6)

- Graph: A curve starting at $(-2, 3)$, decreasing to $(3, -1)$, smooth curve.
- Domain: $[-2, 3]$
- Range: $[-1, 3]$
- Function? Yes (passes vertical line test)
- Type: Continuous

✔ Answer:
Domain: $[-2, 3]$
Range: $[-1, 3]$
Function? Yes
Type: Continuous

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7)

- Graph: A circle centered at origin, radius 2
- Domain: $[-2, 2]$
- Range: $[-2, 2]$
- Function? No (fails vertical line test — e.g., at $x=0$, two y-values)
- Type: Neither (but actually continuous if we consider the full shape; however, since it's not a function, we classify based on points)

But note: It's a circle, so it's not a function.

✔ Answer:
Domain: $[-2, 2]$
Range: $[-2, 2]$
Function? No
Type: Neither (or sometimes said "continuous" but not a function — best to say neither for classification)

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8)

- Graph: A W-shaped graph (like a parabola flipped), from $x = -3$ to $x = 3$, goes down, up, down, up
- Domain: $[-3, 3]$
- Range: $[0, 4]$ (bottoms at $y=0$, tops at $y=4$)
- Function? Yes (each x has only one y)
- Type: Continuous

✔ Answer:
Domain: $[-3, 3]$
Range: $[0, 4]$
Function? Yes
Type: Continuous

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9)

- Graph: A V-shape, but mirrored: starts at $(-4, 2)$, goes down to $(0, -2)$, then up to $(4, 2)$
- Domain: $[-4, 4]$
- Range: $[-2, 2]$
- Function? Yes (passes vertical line test)
- Type: Continuous

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

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10)

- Graph: A series of disconnected line segments forming a zigzag from left to right
- Points: Starts at $(-3, -2)$, up to $(-1, 2)$, down to $(1, -2)$, up to $(3, 2)$
- Domain: $[-3, 3]$ (but only specific intervals)
- But it's disconnected — multiple segments
- Domain: $[-3, 3]$ (all x-values covered)
- Range: $[-2, 2]$
- Function? Yes (each x has only one y)
- Type: Continuous? No — it's discrete? Wait: it's piecewise connected, so it's continuous within segments, but overall not continuous due to gaps?

Wait — look closely: Are the segments connected?

From $(-3,-2)$ to $(-1,2)$: connected
Then from $(-1,2)$ to $(1,-2)$: connected
Then from $(1,-2)$ to $(3,2)$: connected

So it's one continuous path — even though it zigzags.

So yes, continuous

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

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11)

- Graph: A broken line from $(-3, -2)$ to $(-1, 2)$, then from $(-1, 2)$ to $(1, -2)$, then from $(1, -2)$ to $(3, 2)$
- Same as #10? Wait — actually looks like same shape — but let's see:
- Actually, this one might be the same as #10? Or slightly different?

Wait — looking again:
It appears to be a zigzag, but with a gap between $(-1,2)$ and $(1,-2)$? No — seems connected.

Actually, both #10 and #11 seem similar.

But wait — in #11, the line from $(-1,2)$ to $(1,-2)$ may have a break?

No — it's drawn as connected lines.

Wait — perhaps they're the same? Let me assume #11 is different.

Looking carefully: #11 shows a V shape going up, then down, then up — but not symmetric.

But regardless, if it's a connected path, it's continuous.

Assuming it's a piecewise linear path without gaps.

So:

- Domain: $[-3, 3]$
- Range: $[-2, 2]$
- Function? Yes (passes vertical line test)
- Type: Continuous

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

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12)

- Graph: Two diagonal lines crossing at center, forming an “X” shape
- Points: Lines from $(-3, -3)$ to $(3, 3)$, and from $(-3, 3)$ to $(3, -3)$
- So it's two diagonals crossing
- Domain: $[-3, 3]$
- Range: $[-3, 3]$
- Function? No — because at $x=0$, there are two y-values ($y=0$ and $y=0$? Wait — at $x=0$, both lines pass through $(0,0)$ — same point.

Wait — actually, both lines pass through origin.

But for $x=1$: one line gives $y=1$, other gives $y=-1$

So at $x=1$, two outputs → fails vertical line test.

Thus, not a function

- Type: Continuous (lines are continuous), but not a function

✔ Answer:
Domain: $[-3, 3]$
Range: $[-3, 3]$
Function? No
Type: Continuous (but not a function)

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Final Answers Summary:

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

> Note: For #12, although it's continuous, it's not a function because it fails the vertical line test.

Let me know if you want these filled into the worksheet format!