SOLUTION: 1 1 alg2h domain range interval notation - Studypool - Free Printable

To solve the problem of finding the domain and range of each graph and expressing the answers in interval notation, we need to analyze each graph step by step. Here's the detailed solution for each graph:

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Graph 1:

#### Description:
- The graph is a straight line with open circles at the endpoints.
- The line starts at \( (-2, 1) \) and ends at \( (4, 6) \).

#### Domain:
- The \( x \)-values range from \(-2\) to \(4\), but since there are open circles at both endpoints, the domain does not include \(-2\) and \(4\).
- Domain: \( (-2, 4) \)

#### Range:
- The \( y \)-values range from \(1\) to \(6\), but since there are open circles at both endpoints, the range does not include \(1\) and \(6\).
- Range: \( (1, 6) \)

#### Answer:
- Domain: \( (-2, 4) \)
- Range: \( (1, 6) \)

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Graph 2:

#### Description:
- The graph is a piecewise function with three segments.
- The function starts at \( (-3, -2) \), goes down to \( (-2, 0) \), then down to \( (1, -4) \), and finally up to \( (2, -1) \).
- There are open circles at \( (-2, 0) \) and \( (2, -1) \).

#### Domain:
- The \( x \)-values range from \(-3\) to \(2\), including \(-3\) but excluding \(2\).
- Domain: \( [-3, 2) \)

#### Range:
- The \( y \)-values range from \(-4\) to \(0\), including \(-4\) but excluding \(0\).
- Range: \( [-4, 0) \)

#### Answer:
- Domain: \( [-3, 2) \)
- Range: \( [-4, 0) \)

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Graph 3:

#### Description:
- The graph is a downward-opening parabola.
- The vertex is at \( (2, 3) \).
- The parabola extends infinitely downward and covers all \( x \)-values from \(-1\) to \(5\).

#### Domain:
- The \( x \)-values range from \(-1\) to \(5\), inclusive.
- Domain: \( [-1, 5] \)

#### Range:
- The \( y \)-values start at the vertex \( (2, 3) \) and extend downward to \(-6\).
- Range: \( [-6, 3] \)

#### Answer:
- Domain: \( [-1, 5] \)
- Range: \( [-6, 3] \)

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Graph 4:

#### Description:
- The graph is a curve that starts at \( (-2, -1) \) and approaches \( y = 2 \) as \( x \) increases.
- There is an open circle at \( (-2, -1) \).

#### Domain:
- The \( x \)-values start at \(-2\) (exclusive) and extend to infinity.
- Domain: \( (-2, \infty) \)

#### Range:
- The \( y \)-values start at \(-1\) (inclusive) and approach \(2\) (exclusive).
- Range: \( [-1, 2) \)

#### Answer:
- Domain: \( (-2, \infty) \)
- Range: \( [-1, 2) \)

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Graph 5:

#### Description:
- The graph is a curve that starts below the \( x \)-axis, crosses it, and rises above the \( x \)-axis.
- There is an open circle at the bottom point.

#### Domain:
- The \( x \)-values range from \(-1\) to \(1\), inclusive.
- Domain: \( [-1, 1] \)

#### Range:
- The \( y \)-values range from \(-2\) to \(3\), inclusive.
- Range: \( [-2, 3] \)

#### Answer:
- Domain: \( [-1, 1] \)
- Range: \( [-2, 3] \)

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Graph 6:

#### Description:
- The graph is a sinusoidal wave that oscillates between \( y = -2 \) and \( y = 2 \).
- The wave starts at \( (-4, -2) \) and ends at \( (5, -2) \).

#### Domain:
- The \( x \)-values range from \(-4\) to \(5\), inclusive.
- Domain: \( [-4, 5] \)

#### Range:
- The \( y \)-values oscillate between \(-2\) and \(2\), inclusive.
- Range: \( [-2, 2] \)

#### Answer:
- Domain: \( [-4, 5] \)
- Range: \( [-2, 2] \)

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Final Answers:

1. Domain: \( (-2, 4) \), Range: \( (1, 6) \)
2. Domain: \( [-3, 2) \), Range: \( [-4, 0) \)
3. Domain: \( [-1, 5] \), Range: \( [-6, 3] \)
4. Domain: \( (-2, \infty) \), Range: \( [-1, 2) \)
5. Domain: \( [-1, 1] \), Range: \( [-2, 3] \)
6. Domain: \( [-4, 5] \), Range: \( [-2, 2] \)

\[
\boxed{
\begin{array}{ll}
1. & \text{Domain: } (-2, 4), \text{ Range: } (1, 6) \\
2. & \text{Domain: } [-3, 2), \text{ Range: } [-4, 0) \\
3. & \text{Domain: } [-1, 5], \text{ Range: } [-6, 3] \\
4. & \text{Domain: } (-2, \infty), \text{ Range: } [-1, 2) \\
5. & \text{Domain: } [-1, 1], \text{ Range: } [-2, 3] \\
6. & \text{Domain: } [-4, 5], \text{ Range: } [-2, 2] \\
\end{array}
}
\]