Algebra II/Trig Practice 4.1 Domain/Range State the domain of the ... - Free Printable

To determine whether a given graph represents a function or not a function, we use the vertical line test. The vertical line test states:

- If any vertical line intersects the graph at more than one point, then the graph does not represent a function.
- If every vertical line intersects the graph at most one point, then the graph represents a function.

Let's analyze each graph step by step:

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Graph 1:

- The graph is a horizontal line.
- A vertical line will intersect this graph at exactly one point.
- Conclusion: Function

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Graph 2:

- The graph is a straight diagonal line.
- A vertical line will intersect this graph at exactly one point.
- Conclusion: Function

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Graph 3:

- The graph is a parabola that opens to the right.
- A vertical line can intersect this graph at two points (for example, near the vertex).
- Conclusion: Not a Function

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Graph 4:

- The graph is a curve that loops back on itself.
- A vertical line can intersect this graph at two points (near the loop).
- Conclusion: Not a Function

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Graph 5:

- The graph is a piecewise linear function with jumps.
- A vertical line will intersect this graph at exactly one point.
- Conclusion: Function

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Graph 6:

- The graph is a parabola that opens upwards.
- A vertical line will intersect this graph at exactly one point.
- Conclusion: Function

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Graph 7:

- The graph is an "X" shape (two lines crossing).
- A vertical line can intersect this graph at two points (where the lines cross).
- Conclusion: Not a Function

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Graph 8:

- The graph is a V-shaped absolute value function.
- A vertical line will intersect this graph at exactly one point.
- Conclusion: Function

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Graph 9:

- The graph is a zigzag line.
- A vertical line will intersect this graph at exactly one point.
- Conclusion: Function

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Final Answers:

1. Function
2. Function
3. Not a Function
4. Not a Function
5. Function
6. Function
7. Not a Function
8. Function
9. Function

Boxed Answer:

\[
\boxed{
\begin{array}{ccc}
1) \text{Function} & 2) \text{Function} & 3) \text{Not a Function} \\
4) \text{Not a Function} & 5) \text{Function} & 6) \text{Function} \\
7) \text{Not a Function} & 8) \text{Function} & 9) \text{Function}
\end{array}
}
\]