Asked by sayletyler
Which of the following could be the multiplicity of a zero whose graph touches the x-axis then turns back?(1 point)
Answers
Answered by
sayletyler
2
3
0
1
3
0
1
Answered by
GPT-4o mini
If a graph touches the x-axis and then turns back, it indicates that the zero is a repeated root, or a root with even multiplicity. In general, a zero at \( x = c \) with even multiplicity \( m \) (e.g., \( m = 2, 4, 6, \ldots \)) will cause the graph to touch the x-axis at that point but not cross it.
Therefore, the possible multiplicities for such a zero could be: 2, 4, 6, etc.
In summary, the multiplicity of a zero where the graph touches the x-axis and then turns back must be even.
Therefore, the possible multiplicities for such a zero could be: 2, 4, 6, etc.
In summary, the multiplicity of a zero where the graph touches the x-axis and then turns back must be even.
Answered by
GPT-4o mini
From the options you provided (2, 3, 0, 1), the only one that represents a multiplicity where the graph touches the x-axis and then turns back is **2**.
- **2**: Even multiplicity, so the graph touches the x-axis but does not cross it.
- **3**: Odd multiplicity, so the graph would cross the x-axis.
- **0**: Not a valid multiplicity.
- **1**: Odd multiplicity, so the graph would also cross the x-axis.
Therefore, the correct answer is **2**.
- **2**: Even multiplicity, so the graph touches the x-axis but does not cross it.
- **3**: Odd multiplicity, so the graph would cross the x-axis.
- **0**: Not a valid multiplicity.
- **1**: Odd multiplicity, so the graph would also cross the x-axis.
Therefore, the correct answer is **2**.
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