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A coordinate plane's axes range from negative 10 to 10 by 1-unit increments. Two rays are plotted. The first ray starts from an open endpoint, while the second ray starts from a closed endpoint.
Choose the correct piecewise function.
(1 point)
Responses
y={−2, x>03, x>0
y equals left brace line 1 negative 2 comma x greater than 0 line 2 3 comma x less than 0
y={−2x3x
y equals left brace line 1 negative 2 time x line 2 3 times x
y={−2, x<03, x≥0
y equals left brace line 1 negative 2 comma x less than zero line 2 3 comma x less than or equal to zero
y={−2, x>23, x≤3
A coordinate plane's axes range from negative 10 to 10 by 1-unit increments. Two rays are plotted. The first ray starts from an open endpoint, while the second ray starts from a closed endpoint.
Choose the correct piecewise function.
(1 point)
Responses
y={−2, x>03, x>0
y equals left brace line 1 negative 2 comma x greater than 0 line 2 3 comma x less than 0
y={−2x3x
y equals left brace line 1 negative 2 time x line 2 3 times x
y={−2, x<03, x≥0
y equals left brace line 1 negative 2 comma x less than zero line 2 3 comma x less than or equal to zero
y={−2, x>23, x≤3
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine the correct piecewise function based on the description provided:
- The first ray starts from an **open endpoint**. This means that the value associated with this ray is not included in the piecewise function. If we denote this ray as resulting in a constant value of `-2`, it will be for values of \(x > 0\).
- The second ray starts from a **closed endpoint**. This suggests that the corresponding value (3) is included, applicable for \(x \geq 0\).
Given these interpretations, we can analyze the possible responses:
1. **y={−2, x>03, x>0:**
- This means \(y = -2\) for \(x > 0\) and \(y = 3\) for \(x > 0\). This is inconsistent since both cannot be true.
2. **y={−2x3x:**
- This suggests some form of multiplication, but it lacks clear separation of conditions. Therefore, it is not correctly formatted.
3. **y={−2, x<03, x≥0:**
- This means \(y = -2\) for \(x < 0\) (which is consistent with the ray starting from the left side) and \(y = 3\) for \(x \geq 0\) (which is consistent with the ray originating from a closed point on the right). This interpretation fits the description well.
4. **y={−2, x>23, x≤3:**
- This means \(y = -2\) for \(x > 2\) (which does not match the left ray description) and \(y = 3\) for \(x \leq 3\) (which is also too broad for the ray starting from the closed point).
Considering the above analysis, the correct piecewise function is:
**y={−2, x<03, x≥0.**
- The first ray starts from an **open endpoint**. This means that the value associated with this ray is not included in the piecewise function. If we denote this ray as resulting in a constant value of `-2`, it will be for values of \(x > 0\).
- The second ray starts from a **closed endpoint**. This suggests that the corresponding value (3) is included, applicable for \(x \geq 0\).
Given these interpretations, we can analyze the possible responses:
1. **y={−2, x>03, x>0:**
- This means \(y = -2\) for \(x > 0\) and \(y = 3\) for \(x > 0\). This is inconsistent since both cannot be true.
2. **y={−2x3x:**
- This suggests some form of multiplication, but it lacks clear separation of conditions. Therefore, it is not correctly formatted.
3. **y={−2, x<03, x≥0:**
- This means \(y = -2\) for \(x < 0\) (which is consistent with the ray starting from the left side) and \(y = 3\) for \(x \geq 0\) (which is consistent with the ray originating from a closed point on the right). This interpretation fits the description well.
4. **y={−2, x>23, x≤3:**
- This means \(y = -2\) for \(x > 2\) (which does not match the left ray description) and \(y = 3\) for \(x \leq 3\) (which is also too broad for the ray starting from the closed point).
Considering the above analysis, the correct piecewise function is:
**y={−2, x<03, x≥0.**
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