Domain and Range Worksheet: Practice Finding Domains and Ranges - Free Printable

To solve the problem of finding the domain and range for each function in the provided images, we need to analyze each graph carefully. Here's a step-by-step explanation:

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Definitions:

1. Domain: The set of all possible input values (x-values) for which the function is defined.
2. Range: The set of all possible output values (y-values) that the function can produce.

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Step-by-Step Analysis for Each Graph:

#### Graph 1:
- Domain: The x-values extend from approximately \(-3\) to \(3\). Therefore, the domain is:
\[
[-3, 3]
\]
- Range: The y-values extend from approximately \(-2\) to \(4\). Therefore, the range is:
\[
[-2, 4]
\]

#### Graph 2:
- Domain: The x-values extend from approximately \(-4\) to infinity (\(\infty\)). Therefore, the domain is:
\[
[-4, \infty)
\]
- Range: The y-values extend from approximately \(-3\) to infinity (\(\infty\)). Therefore, the range is:
\[
[-3, \infty)
\]

#### Graph 3:
- Domain: The x-values extend from approximately \(-5\) to \(5\). Therefore, the domain is:
\[
[-5, 5]
\]
- Range: The y-values extend from approximately \(-2\) to \(4\). Therefore, the range is:
\[
[-2, 4]
\]

#### Graph 4:
- Domain: The x-values extend from approximately \(-4\) to \(4\). Therefore, the domain is:
\[
[-4, 4]
\]
- Range: The y-values extend from approximately \(-3\) to \(3\). Therefore, the range is:
\[
[-3, 3]
\]

#### Graph 5:
- Domain: The x-values extend from approximately \(-6\) to \(0\). Therefore, the domain is:
\[
[-6, 0]
\]
- Range: The y-values extend from approximately \(-4\) to \(2\). Therefore, the range is:
\[
[-4, 2]
\]

#### Graph 6:
- Domain: The x-values are discrete points at \(-4\), \(-2\), \(0\), \(2\), and \(4\). Therefore, the domain is:
\[
\{-4, -2, 0, 2, 4\}
\]
- Range: The y-values are discrete points at \(-3\), \(-1\), \(1\), and \(3\). Therefore, the range is:
\[
\{-3, -1, 1, 3\}
\]

#### Graph 7:
- Domain: The x-values are discrete points at \(-3\), \(-1\), \(1\), and \(3\). Therefore, the domain is:
\[
\{-3, -1, 1, 3\}
\]
- Range: The y-values are discrete points at \(-2\), \(0\), and \(2\). Therefore, the range is:
\[
\{-2, 0, 2\}
\]

#### Graph 8:
- Domain: The x-values extend from negative infinity (\(-\infty\)) to positive infinity (\(\infty\)). Therefore, the domain is:
\[
(-\infty, \infty)
\]
- Range: The y-values extend from approximately \(-2\) to infinity (\(\infty\)). Therefore, the range is:
\[
[-2, \infty)
\]

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Final Answers:

1. Domain: \([-3, 3]\), Range: \([-2, 4]\)
2. Domain: \([-4, \infty)\), Range: \([-3, \infty)\)
3. Domain: \([-5, 5]\), Range: \([-2, 4]\)
4. Domain: \([-4, 4]\), Range: \([-3, 3]\)
5. Domain: \([-6, 0]\), Range: \([-4, 2]\)
6. Domain: \(\{-4, -2, 0, 2, 4\}\), Range: \(\{-3, -1, 1, 3\}\)
7. Domain: \(\{-3, -1, 1, 3\}\), Range: \(\{-2, 0, 2\}\)
8. Domain: \((-∞, ∞)\), Range: \([-2, ∞)\)

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Boxed Final Answer:

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