The figure on the right shows 6 semicircles with center at $( 1,1 )$ and radii of lengths $\frac { 1 } { 3 } , \frac { 2 } { 3 } , 1 , \frac { 4 } { 3 } , \frac { 5 } { 3 } , 2$ respectively. Three functions $$\begin{aligned}
& y = \log _ { \frac { 1 } { 4 } } x \\
& y = \left( \frac { 2 } { 3 } \right) ^ { x } \\
& y = 3 ^ { x }
\end{aligned}$$ Let $a , b , c$ be the number of intersection points where the graphs of these functions meet the semicircles, respectively. Which of the following correctly represents the relationship between $a , b , c$? (Here, $x \geqq 1$ and the semicircles include the endpoints of the diameter.) [4 points] (1) $a < b < c$ (2) $a < c < b$ (3) $b < c < a$ (4) $c < a < b$ (5) $c < b < a$
The figure on the right shows 6 semicircles with center at $( 1,1 )$ and radii of lengths $\frac { 1 } { 3 } , \frac { 2 } { 3 } , 1 , \frac { 4 } { 3 } , \frac { 5 } { 3 } , 2$ respectively. Three functions
$$\begin{aligned}
& y = \log _ { \frac { 1 } { 4 } } x \\
& y = \left( \frac { 2 } { 3 } \right) ^ { x } \\
& y = 3 ^ { x }
\end{aligned}$$
Let $a , b , c$ be the number of intersection points where the graphs of these functions meet the semicircles, respectively. Which of the following correctly represents the relationship between $a , b , c$?\\
(Here, $x \geqq 1$ and the semicircles include the endpoints of the diameter.) [4 points]\\
(1) $a < b < c$\\
(2) $a < c < b$\\
(3) $b < c < a$\\
(4) $c < a < b$\\
(5) $c < b < a$