To solve the problem, we need to determine whether each graph represents a function and, if it does, whether it is a one-to-one function. Let's analyze each graph step by step.
Graph 1:
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Shape: A circle.
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Vertical Line Test: A vertical line can intersect the circle at more than one point. For example, a vertical line passing through the center of the circle will intersect it at two points.
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Conclusion: This graph does not pass the vertical line test, so it is
not a function.
Answer for Graph 1:
- Not a function
Graph 2:
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Shape: A parabola opening downwards.
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Vertical Line Test: A vertical line will intersect the parabola at most once. Therefore, it passes the vertical line test.
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Horizontal Line Test: A horizontal line can intersect the parabola at more than one point. For example, a horizontal line at \( y = 0 \) will intersect the parabola at two points.
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Conclusion: This graph is a function but
not one-to-one because it fails the horizontal line test.
Answer for Graph 2:
- Function, not one-to-one.
Graph 3:
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Shape: A cubic-like curve.
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Vertical Line Test: A vertical line will intersect the curve at most once. Therefore, it passes the vertical line test.
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Horizontal Line Test: A horizontal line will intersect the curve at most once. For example, no horizontal line will intersect the curve at more than one point.
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Conclusion: This graph is a function and
one-to-one because it passes both the vertical and horizontal line tests.
Answer for Graph 3:
- One-to-one function
Graph 4:
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Shape: A semicircle (upper half of a circle).
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Vertical Line Test: A vertical line will intersect the semicircle at most once. Therefore, it passes the vertical line test.
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Horizontal Line Test: A horizontal line will intersect the semicircle at most once. For example, no horizontal line will intersect the semicircle at more than one point.
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Conclusion: This graph is a function and
one-to-one because it passes both the vertical and horizontal line tests.
Answer for Graph 4:
- One-to-one function
Final Answers:
1. Not a function
2. Function, not one-to-one
3. One-to-one function
4. One-to-one function
\[
\boxed{
\begin{array}{ll}
1. & \text{Not a function} \\
2. & \text{Function, not one-to-one} \\
3. & \text{One-to-one function} \\
4. & \text{One-to-one function}
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of one to one function worksheet.
