csat-suneung 2007 Q9

csat-suneung · South-Korea · csat__math-science 4 marks
In the coordinate plane, let $C$ be a circle with center $(0,3)$ and radius 1. For a positive number $r$, let $f ( r )$ be the number of circles with radius $r$ that meet circle $C$ at exactly one point and are tangent to the $x$-axis. Which of the following statements in are correct? [4 points]
Remarks ㄱ. $f ( 2 ) = 3$ ㄴ. $\lim _ { r \rightarrow 1 + 0 } f ( r ) = f ( 1 )$ ㄷ. The number of discontinuity points of the function $f ( r )$ on the interval $( 0,4 )$ is 2.
(1) ㄱ
(2) ㄴ
(3) ㄷ
(4) ㄱ, ㄷ
(5) ㄱ, ㄴ, ㄷ
In the coordinate plane, let $C$ be a circle with center $(0,3)$ and radius 1. For a positive number $r$, let $f ( r )$ be the number of circles with radius $r$ that meet circle $C$ at exactly one point and are tangent to the $x$-axis. Which of the following statements in <Remarks> are correct? [4 points]

\textbf{Remarks}\\
ㄱ. $f ( 2 ) = 3$\\
ㄴ. $\lim _ { r \rightarrow 1 + 0 } f ( r ) = f ( 1 )$\\
ㄷ. The number of discontinuity points of the function $f ( r )$ on the interval $( 0,4 )$ is 2.\\
(1) ㄱ\\
(2) ㄴ\\
(3) ㄷ\\
(4) ㄱ, ㄷ\\
(5) ㄱ, ㄴ, ㄷ