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 [tex]\( f(x) \)[/tex] when [tex]\( x = 0 \)[/tex]. The [tex]\( y \)[/tex]-intercept is the point where the graph of the function crosses the [tex]\( y \)[/tex]-axis.
Step-by-Step Solution:
1. Start with the given function:
[tex]\[
f(x) = -\frac{2}{9}x + \frac{1}{3}
\][/tex]
2. Substitute [tex]\( x = 0 \)[/tex] into the function to find the [tex]\( y \)[/tex]-intercept:
[tex]\[
f(0) = -\frac{2}{9}(0) + \frac{1}{3}
\][/tex]
3. Simplify the expression:
[tex]\[
f(0) = 0 + \frac{1}{3}
\][/tex]
4. This simplifies to:
[tex]\[
f(0) = \frac{1}{3}
\][/tex]
Therefore, 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].
So the correct answer is:
[tex]\[
\frac{1}{3}
\][/tex]
