Domain and Range Worksheets - Free Printable

Since I can't view or access images directly, I can’t see the specific graphs on your worksheet. However, I can guide you through how to solve each problem step by step based on standard graph analysis.

Here’s a complete explanation of how to determine:

1. Domain
2. Range
3. Whether the graph is a function (using the Vertical Line Test)
4. Whether it's discrete, continuous, or neither

---

🔍 Step-by-Step Guide for Each Graph

#### ✔ 1. Domain
- The domain is the set of all x-values (horizontal extent) that the graph covers.
- Look at the leftmost and rightmost points.
- If the graph extends infinitely in one direction, use infinity (∞).
- Write in interval notation or set notation.

#### ✔ 2. Range
- The range is the set of all y-values (vertical extent) that the graph covers.
- Look at the lowest and highest points.
- Use interval notation.

#### ✔ 3. Is it a function?
- Use the Vertical Line Test:
- Draw vertical lines across the graph.
- If any vertical line crosses the graph more than once, it’s not a function.
- If every vertical line crosses at most once → Yes, it’s a function.

#### ✔ 4. Discrete, Continuous, or Neither?
- Discrete: Points are separate (like dots), not connected.
- Continuous: A smooth, unbroken curve or line (no breaks).
- Neither: Mixed or undefined behavior (e.g., jumps with gaps).

---

Now let’s go through each problem as if we could see the graphs. I’ll give you typical answers based on common types of graphs found in such worksheets.

---

📊 Problem-by-Problem Analysis (Typical Examples)

> Note: These answers are *examples* based on common graph types. You should adjust them based on your actual image.

---

#### 1)
- Graph: A downward parabola opening from top to bottom.
- Domain: All real numbers: $(-\infty, \infty)$
- Range: From vertex down: $(-\infty, 4]$
- Function? Yes (passes vertical line test)
- Type: Continuous

---

#### 2)
- Graph: A wavy line (like sine wave) with peaks and valleys.
- Domain: $[-3, 3]$
- Range: $[-2, 2]$
- Function? Yes
- Type: Continuous

---

#### 3)
- Graph: A U-shaped parabola opening upward.
- Domain: $(-\infty, \infty)$
- Range: $[0, \infty)$
- Function? Yes
- Type: Continuous

---

#### 4)
- Graph: A horizontal line segment from $x = -2$ to $x = 2$, at $y = 1$
- Domain: $[-2, 2]$
- Range: $\{1\}$ (just one y-value)
- Function? Yes
- Type: Continuous

---

#### 5)
- Graph: Scattered points (e.g., (-2, 3), (-1, 1), (0, 2), (1, 0), (2, 1))
- Domain: $\{-2, -1, 0, 1, 2\}$
- Range: $\{0, 1, 2, 3\}$
- Function? Yes (each x has only one y)
- Type: Discrete

---

#### 6)
- Graph: A curved line going from left to right, like a sideways "S" or exponential decay.
- Domain: $(-\infty, 2]$
- Range: $[-3, 1]$
- Function? Yes
- Type: Continuous

---

#### 7)
- Graph: A circle centered at origin with radius 2.
- Domain: $[-2, 2]$
- Range: $[-2, 2]$
- Function? No (fails vertical line test — multiple y-values for same x)
- Type: Neither (it's a relation, not a function)

---

#### 8)
- Graph: A zigzag line (like a sawtooth) from $x = -2$ to $x = 2$, oscillating up and down.
- Domain: $[-2, 2]$
- Range: $[-2, 2]$
- Function? Yes
- Type: Continuous

---

#### 9)
- Graph: A V-shape pointing down, but with two branches from same x-value (e.g., looks like an upside-down “V” split).
- Domain: $[-3, 3]$
- Range: $[-3, 1]$
- Function? No (fails vertical line test — e.g., at $x = 0$, two y-values)
- Type: Neither

---

#### 10)
- Graph: A triangle-like shape with vertices at $(-2, 0)$, $(0, 2)$, $(2, 0)$
- Domain: $[-2, 2]$
- Range: $[0, 2]$
- Function? Yes (each x maps to one y)
- Type: Continuous

---

#### 11)
- Graph: A broken line with open and closed circles (e.g., piecewise)
- Domain: $[-2, 2]$ (check endpoints)
- Range: $[0, 2]$
- Function? Yes (even with open circles, no x has two outputs)
- Type: Continuous (if connected), or discrete if just points — but likely continuous

---

#### 12)
- Graph: A triangle pointing to the right (like a sideways V), with base along x-axis.
- Domain: $[-2, 2]$
- Range: $[0, 2]$
- Function? No (fails vertical line test — e.g., at $x = 0$, two y-values)
- Type: Neither

---

✔ Summary Table (Example Answers)

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

---

🛠️ How to Apply This to Your Worksheet:

1. For each graph, look at:
- Left/right bounds → Domain
- Top/bottom bounds → Range
2. Use Vertical Line Test → Is it a function?
3. Are points isolated? → Discrete
- Connected smoothly? → Continuous
- Mixed or fails both? → Neither

---

If you can describe any of the graphs (e.g., "a circle", "a zigzag line", "dots at (-2,1), (-1,2), etc."), I can help you analyze them specifically!

Let me know which ones you're unsure about.