To find the [tex]\( y \)[/tex]-intercept of the function [tex]\( f(x) = -\frac{2}{9} x + \frac{1}{3} \)[/tex], we need to determine the value of the function when [tex]\( x = 0 \)[/tex].
The [tex]\( y \)[/tex]-intercept of a function is the point where the graph of the function crosses the [tex]\( y \)[/tex]-axis. This happens when [tex]\( x = 0 \)[/tex].
By substituting [tex]\( x = 0 \)[/tex] into the function [tex]\( f(x) = -\frac{2}{9} x + \frac{1}{3} \)[/tex]:
[tex]\[ f(0) = -\frac{2}{9} (0) + \frac{1}{3} \][/tex]
Since [tex]\(-\frac{2}{9} (0)\)[/tex] equals 0, the equation simplifies to:
[tex]\[ f(0) = \frac{1}{3} \][/tex]
Hence, the [tex]\( y \)[/tex]-intercept of the function [tex]\( f(x) = -\frac{2}{9} x + \frac{1}{3} \)[/tex] is [tex]\( \frac{1}{3} \)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{\frac{1}{3}} \][/tex]
