e area of a circle can be represented by the function π

Question

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.

Answer 1

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 $r\ge 0$.

2. Behavior of the function: As $r$ increases, the area $A$ also increases. Therefore, the function is always increasing for $r\ge 0$ 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.