Question
e area of a circle can be represented by the function π
with domain
, where
is the radius of the circle. Which statement about this function is true?
A.
The function has a minimum.
B.
The function has two zeros.
C.
The function has no zeros.
D.
The function has a maximum.
with domain
, where
is the radius of the circle. Which statement about this function is true?
A.
The function has a minimum.
B.
The function has two zeros.
C.
The function has no zeros.
D.
The function has a maximum.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To analyze the function representing the area of a circle, which is given by the formula \( A = \pi r^2 \), where \( r \) is the radius of the circle, we need to consider the properties of this function.
1. **Domain**: The radius \( r \) must be non-negative, so the domain of the function is \( r \geq 0 \).
2. **Behavior of the function**: As \( r \) increases, the area \( A \) also increases. Therefore, the function is always increasing for \( r \geq 0 \) and its value is always positive for \( r > 0 \).
3. **Zeros of the function**: The only zero of the function occurs when the area \( A = 0 \). This happens when \( r = 0 \). So, the function has one zero.
4. **Minimum and Maximum**: The function \( A = \pi r^2 \) does reach a minimum value of 0 at \( r = 0 \) but does not have a maximum value since as \( r \) increases, \( A \) keeps increasing indefinitely.
Based on this analysis, the correct statement about the function is:
**A. The function has a minimum.**
This minimum occurs at \( r = 0 \), where the area of the circle is also 0. The function does not have two zeros, has one zero, and does not have a maximum.
1. **Domain**: The radius \( r \) must be non-negative, so the domain of the function is \( r \geq 0 \).
2. **Behavior of the function**: As \( r \) increases, the area \( A \) also increases. Therefore, the function is always increasing for \( r \geq 0 \) and its value is always positive for \( r > 0 \).
3. **Zeros of the function**: The only zero of the function occurs when the area \( A = 0 \). This happens when \( r = 0 \). So, the function has one zero.
4. **Minimum and Maximum**: The function \( A = \pi r^2 \) does reach a minimum value of 0 at \( r = 0 \) but does not have a maximum value since as \( r \) increases, \( A \) keeps increasing indefinitely.
Based on this analysis, the correct statement about the function is:
**A. The function has a minimum.**
This minimum occurs at \( r = 0 \), where the area of the circle is also 0. The function does not have two zeros, has one zero, and does not have a maximum.
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