To find the y-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 y-intercept occurs where the graph of the function crosses the y-axis. This happens when [tex]\( x = 0 \)[/tex].
Let's substitute [tex]\( x = 0 \)[/tex] into the function:
[tex]\[ f(0) = -\frac{2}{9}(0) + \frac{1}{3} \][/tex]
Simplifying this:
[tex]\[ f(0) = 0 + \frac{1}{3} \][/tex]
[tex]\[ f(0) = \frac{1}{3} \][/tex]
Therefore, the y-intercept of the function [tex]\( f(x) = -\frac{2}{9} x + \frac{1}{3} \)[/tex] is [tex]\(\frac{1}{3}\)[/tex].
So, the correct answer is [tex]\(\frac{1}{3}\)[/tex].
