To find the [tex]\( y \)[/tex]-intercept of the function [tex]\( f(x) = 3^{x+2} \)[/tex], we need to determine the value of [tex]\( f(x) \)[/tex] when [tex]\( x = 0 \)[/tex].
1. Substitute [tex]\( x = 0 \)[/tex] into the function:
[tex]\[
f(0) = 3^{0+2}
\][/tex]
2. Simplify the exponent:
[tex]\[
0 + 2 = 2
\][/tex]
3. Evaluate the power of 3:
[tex]\[
3^2 = 9
\][/tex]
Thus, the [tex]\( y \)[/tex]-intercept of the function [tex]\( f(x) = 3^{x+2} \)[/tex] is the point where [tex]\( x = 0 \)[/tex] and [tex]\( y = 9 \)[/tex]. Therefore, the [tex]\( y \)[/tex]-intercept is the point [tex]\((0, 9)\)[/tex].
So, the correct answer is:
B. [tex]\((0, 9)\)[/tex]
