Domain and Range Worksheet 1 General Domain and Range Worksheet ... - Free Printable

Since I can't view or access uploaded images directly, I can't see the specific graphs in your worksheet. However, I can help you solve Domain and Range Worksheet #1 based on typical problems of this type.

Below is a step-by-step guide to solving each problem like those on your worksheet, along with explanations for how to determine:

- Domain: All possible x-values (input values) for which the function is defined.
- Range: All possible y-values (output values) that the function can produce.
- Function?: Use the Vertical Line Test — if any vertical line intersects the graph more than once, it's not a function.
- Discrete vs Continuous:
- Discrete: Points are separate and not connected (like dots).
- Continuous: The graph is a connected curve or line (no breaks).

---

Let’s go through each question as if they were standard types found on such worksheets. Since I don’t have the actual image, I’ll describe common patterns and give examples.

---

General Strategy

1. Domain: Look at the leftmost and rightmost points on the graph. The domain is all x-values from left to right.
- Use interval notation: e.g., $[-3, 5]$, $(-\infty, \infty)$, etc.
2. Range: Look at the lowest and highest y-values on the graph.
3. Function?: Draw imaginary vertical lines. If any line hits two points, it's not a function.
4. Discrete/Continuous:
- Discrete: Points are isolated (e.g., plotted dots).
- Continuous: A solid line or curve.

---

Now, let’s assume the following typical graphs for each problem (common ones):

---

1) Graph: Vertical line segment from (−2, 0) to (−2, 4)

- Domain: $x = -2$ → $\{-2\}$
- Range: $y$ from 0 to 4 → $[0, 4]$
- Function? No — multiple y-values for same x → fails vertical line test.
- Type: Discrete (if just points), but here it's a line segment — so continuous but not a function.

> ✔ Answer:
> Domain: $\{-2\}$
> Range: $[0, 4]$
> Function: No
> Type: Continuous (but not a function)

---

2) Graph: Parabola opening upward, vertex at (0, −2), goes up to y=4

- Domain: All real numbers → $(-\infty, \infty)$
- Range: From minimum y-value: $[-2, \infty)$
- Function? Yes — passes vertical line test.
- Type: Continuous

> ✔ Answer:
> Domain: $(-\infty, \infty)$
> Range: $[-2, \infty)$
> Function: Yes
> Type: Continuous

---

3) Graph: Sine-like wave between x = −π and x = π, peaks at y = 2 and y = −2

- Domain: $[-\pi, \pi]$
- Range: $[-2, 2]$
- Function? Yes — one output per input.
- Type: Continuous

> ✔ Answer:
> Domain: $[-\pi, \pi]$
> Range: $[-2, 2]$
> Function: Yes
> Type: Continuous

---

4) Graph: Horizontal line segment from (−3, 2) to (3, 2)

- Domain: $[-3, 3]$
- Range: $[2, 2] = \{2\}$
- Function? Yes — every x has only one y.
- Type: Continuous

> ✔ Answer:
> Domain: $[-3, 3]$
> Range: $\{2\}$
> Function: Yes
> Type: Continuous

---

5) Graph: Two disconnected points: (−2, 1), (0, 3), (2, 1)

- Domain: $\{-2, 0, 2\}$
- Range: $\{1, 3\}$
- Function? Yes — no repeated x-values.
- Type: Discrete

> ✔ Answer:
> Domain: $\{-2, 0, 2\}$
> Range: $\{1, 3\}$
> Function: Yes
> Type: Discrete

---

6) Graph: Semi-circle, top half, center at origin, radius 2

- Domain: $[-2, 2]$
- Range: $[0, 2]$
- Function? Yes — top half of circle passes vertical line test.
- Type: Continuous

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

---

7) Graph: Circle centered at origin, radius 2

- Domain: $[-2, 2]$
- Range: $[-2, 2]$
- Function? No — vertical line through center hits two points.
- Type: Continuous

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

---

8) Graph: Wavy line (like sine wave) from x = 0 to x = 4, oscillating

- Domain: $[0, 4]$
- Range: depends on amplitude — say $[-1, 1]$
- Function? Yes
- Type: Continuous

> ✔ Answer:
> Domain: $[0, 4]$
> Range: $[-1, 1]$
> Function: Yes
> Type: Continuous

---

9) Graph: Two vertical line segments: (−1, 0) to (−1, 2), and (1, 0) to (1, 2)

- Domain: $\{-1, 1\}$
- Range: $[0, 2]$
- Function? No — both x = −1 and x = 1 have multiple y-values → fails vertical line test.
- Type: Continuous (segments), but not a function

> ✔ Answer:
> Domain: $\{-1, 1\}$
> Range: $[0, 2]$
> Function: No
> Type: Continuous

---

10) Graph: V-shaped absolute value graph, vertex at (0,0), opens up

- Domain: $(-\infty, \infty)$
- Range: $[0, \infty)$
- Function? Yes
- Type: Continuous

> ✔ Answer:
> Domain: $(-\infty, \infty)$
> Range: $[0, \infty)$
> Function: Yes
> Type: Continuous

---

11) Graph: Step function (like floor function), jumps at integer values

- Domain: $[0, 4]$
- Range: $\{1, 2, 3, 4\}$ — depends on steps
- Function? Yes — each x maps to one y
- Type: Discrete (if steps are not connected), but often shown as continuous steps

> ✔ Answer:
> Domain: $[0, 4]$
> Range: $\{1, 2, 3, 4\}$
> Function: Yes
> Type: Discrete or Continuous depending on drawing — usually discrete if jumps

---

12) Graph: Diagonal line from (0,0) to (4,4), then drops to (4,0)

- Domain: $[0, 4]$
- Range: $[0, 4]$
- Function? Yes — even though it drops, it's still one y per x.
- Type: Continuous

> ✔ Answer:
> Domain: $[0, 4]$
> Range: $[0, 4]$
> Function: Yes
> Type: Continuous

---

✔ Summary Tips:

| Feature | How to Determine |
|--------|------------------|
| Domain | Leftmost to rightmost x-values |
| Range | Lowest to highest y-values |
| Function? | Vertical Line Test |
| Discrete | Isolated points |
| Continuous | Connected line/curve |

---

If you can describe the graphs or list what each one looks like, I can give you exact answers for your worksheet.

For example, tell me:
- "Graph 1 is a straight line from (-2,1) to (3,5)"
- "Graph 5 is a circle"
- "Graph 8 is a parabola opening downward"

Then I’ll fill in the exact domains, ranges, and classifications.

Let me know!