To determine the [tex]\( y \)[/tex]-intercept of the function [tex]\( f(x) = \left(\frac{3}{5}\right)^x \)[/tex], we need to find 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, which occurs at [tex]\( x = 0 \)[/tex].
1. Substitute [tex]\( x = 0 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(0) = \left(\frac{3}{5}\right)^0
\][/tex]
2. Any non-zero number raised to the power of 0 is equal to 1:
[tex]\[
\left(\frac{3}{5}\right)^0 = 1
\][/tex]
3. Thus, the [tex]\( y \)[/tex]-intercept is:
[tex]\[
(0, 1)
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{(0,1)}
\][/tex]
