Worksheet for identifying domain, range, and functions from graphs.

To solve the problem of determining the domain, range, and whether each graph represents a function, we will analyze each graph step by step. Let's go through each one:

---

1)

#### Graph:
- The graph is a set of discrete points.
- Points: \((-3, 2)\), \((-2, 1)\), \((-1, 0)\), \((0, -1)\), \((1, -2)\), \((2, -3)\).

#### Domain:
The domain is the set of all \(x\)-coordinates of the points.
\[ \text{Domain} = \{-3, -2, -1, 0, 1, 2\} \]

#### Range:
The range is the set of all \(y\)-coordinates of the points.
\[ \text{Range} = \{-3, -2, -1, 0, 1, 2\} \]

#### Function:
Since each \(x\)-value corresponds to exactly one \(y\)-value, this is a function.

#### Answer:
\[ \text{Domain: } \{-3, -2, -1, 0, 1, 2\} \]
\[ \text{Range: } \{-3, -2, -1, 0, 1, 2\} \]
\[ \text{Function: Yes} \]

---

2)

#### Graph:
- The graph is a continuous curve.
- The curve starts at \(x = -3\) and ends at \(x = 3\).
- The curve starts at \(y = 2\) and ends at \(y = -2\).

#### Domain:
The domain is the interval of \(x\)-values covered by the curve.
\[ \text{Domain} = [-3, 3] \]

#### Range:
The range is the interval of \(y\)-values covered by the curve.
\[ \text{Range} = [-2, 2] \]

#### Function:
Since the curve passes the vertical line test (no vertical line intersects the curve more than once), this is a function.

#### Answer:
\[ \text{Domain: } [-3, 3] \]
\[ \text{Range: } [-2, 2] \]
\[ \text{Function: Yes} \]

---

3)

#### Graph:
- The graph is a continuous curve.
- The curve starts at \(x = -3\) and ends at \(x = 3\).
- The curve starts at \(y = -2\) and ends at \(y = 2\).

#### Domain:
The domain is the interval of \(x\)-values covered by the curve.
\[ \text{Domain} = [-3, 3] \]

#### Range:
The range is the interval of \(y\)-values covered by the curve.
\[ \text{Range} = [-2, 2] \]

#### Function:
Since the curve passes the vertical line test (no vertical line intersects the curve more than once), this is a function.

#### Answer:
\[ \text{Domain: } [-3, 3] \]
\[ \text{Range: } [-2, 2] \]
\[ \text{Function: Yes} \]

---

4)

#### Graph:
- The graph is a continuous curve.
- The curve starts at \(x = -3\) and ends at \(x = 3\).
- The curve starts at \(y = -2\) and ends at \(y = 2\).

#### Domain:
The domain is the interval of \(x\)-values covered by the curve.
\[ \text{Domain} = [-3, 3] \]

#### Range:
The range is the interval of \(y\)-values covered by the curve.
\[ \text{Range} = [-2, 2] \]

#### Function:
Since the curve does not pass the vertical line test (a vertical line can intersect the curve more than once), this is not a function.

#### Answer:
\[ \text{Domain: } [-3, 3] \]
\[ \text{Range: } [-2, 2] \]
\[ \text{Function: No} \]

---

5)

#### Graph:
- The graph is a continuous curve.
- The curve starts at \(x = -3\) and ends at \(x = 3\).
- The curve starts at \(y = 3\) and ends at \(y = -3\).

#### Domain:
The domain is the interval of \(x\)-values covered by the curve.
\[ \text{Domain} = [-3, 3] \]

#### Range:
The range is the interval of \(y\)-values covered by the curve.
\[ \text{Range} = [-3, 3] \]

#### Function:
Since the curve passes the vertical line test (no vertical line intersects the curve more than once), this is a function.

#### Answer:
\[ \text{Domain: } [-3, 3] \]
\[ \text{Range: } [-3, 3] \]
\[ \text{Function: Yes} \]

---

6)

#### Graph:
- The graph is a continuous curve.
- The curve starts at \(x = -3\) and ends at \(x = 3\).
- The curve starts at \(y = -3\) and ends at \(y = 3\).

#### Domain:
The domain is the interval of \(x\)-values covered by the curve.
\[ \text{Domain} = [-3, 3] \]

#### Range:
The range is the interval of \(y\)-values covered by the curve.
\[ \text{Range} = [-3, 3] \]

#### Function:
Since the curve passes the vertical line test (no vertical line intersects the curve more than once), this is a function.

#### Answer:
\[ \text{Domain: } [-3, 3] \]
\[ \text{Range: } [-3, 3] \]
\[ \text{Function: Yes} \]

---

7)

#### Graph:
- The graph is a straight line.
- The line extends infinitely in both directions.
- The slope is negative.

#### Domain:
The domain is all real numbers since the line extends infinitely in the \(x\)-direction.
\[ \text{Domain} = (-\infty, \infty) \]

#### Range:
The range is all real numbers since the line extends infinitely in the \(y\)-direction.
\[ \text{Range} = (-\infty, \infty) \]

#### Function:
Since the line passes the vertical line test (no vertical line intersects the line more than once), this is a function.

#### Answer:
\[ \text{Domain: } (-\infty, \infty) \]
\[ \text{Range: } (-\infty, \infty) \]
\[ \text{Function: Yes} \]

---

8)

#### Graph:
- The graph is a continuous curve.
- The curve starts at \(x = -3\) and ends at \(x = 3\).
- The curve starts at \(y = -3\) and ends at \(y = 3\).

#### Domain:
The domain is the interval of \(x\)-values covered by the curve.
\[ \text{Domain} = [-3, 3] \]

#### Range:
The range is the interval of \(y\)-values covered by the curve.
\[ \text{Range} = [-3, 3] \]

#### Function:
Since the curve passes the vertical line test (no vertical line intersects the curve more than once), this is a function.

#### Answer:
\[ \text{Domain: } [-3, 3] \]
\[ \text{Range: } [-3, 3] \]
\[ \text{Function: Yes} \]

---

Final Answers:

1. \[
\boxed{
\begin{aligned}
&\text{Domain: } \{-3, -2, -1, 0, 1, 2\} \\
&\text{Range: } \{-3, -2, -1, 0, 1, 2\} \\
&\text{Function: Yes}
\end{aligned}
}
\]

2. \[
\boxed{
\begin{aligned}
&\text{Domain: } [-3, 3] \\
&\text{Range: } [-2, 2] \\
&\text{Function: Yes}
\end{aligned}
}
\]

3. \[
\boxed{
\begin{aligned}
&\text{Domain: } [-3, 3] \\
&\text{Range: } [-2, 2] \\
&\text{Function: Yes}
\end{aligned}
}
\]

4. \[
\boxed{
\begin{aligned}
&\text{Domain: } [-3, 3] \\
&\text{Range: } [-2, 2] \\
&\text{Function: No}
\end{aligned}
}
\]

5. \[
\boxed{
\begin{aligned}
&\text{Domain: } [-3, 3] \\
&\text{Range: } [-3, 3] \\
&\text{Function: Yes}
\end{aligned}
}
\]

6. \[
\boxed{
\begin{aligned}
&\text{Domain: } [-3, 3] \\
&\text{Range: } [-3, 3] \\
&\text{Function: Yes}
\end{aligned}
}
\]

7. \[
\boxed{
\begin{aligned}
&\text{Domain: } (-\infty, \infty) \\
&\text{Range: } (-\infty, \infty) \\
&\text{Function: Yes}
\end{aligned}
}
\]

8. \[
\boxed{
\begin{aligned}
&\text{Domain: } [-3, 3] \\
&\text{Range: } [-3, 3] \\
&\text{Function: Yes}
\end{aligned}
}
\]