To find the [tex]\( y \)[/tex]-intercept of the function [tex]\( f(x) = 3^{x+2} \)[/tex], we need to determine the value of the function when [tex]\( x = 0 \)[/tex].
1. Start by substituting [tex]\( x = 0 \)[/tex] into the function [tex]\( f(x) = 3^{x+2} \)[/tex]:
[tex]\[
f(0) = 3^{0+2}
\][/tex]
2. Simplify the exponent:
[tex]\[
f(0) = 3^2
\][/tex]
3. Evaluate [tex]\( 3^2 \)[/tex]:
[tex]\[
3^2 = 9
\][/tex]
Therefore, when [tex]\( x = 0 \)[/tex], [tex]\( f(x) = 9 \)[/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]\( (0, f(0)) \)[/tex]. Hence, the [tex]\( y \)[/tex]-intercept is [tex]\( (0, 9) \)[/tex].
The correct answer is:
B. [tex]\((0, 9)\)[/tex]
