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]. The [tex]\( y \)[/tex]-intercept is the point where the graph of the function crosses the y-axis, which occurs when [tex]\( x = 0 \)[/tex].
Step-by-step solution:
1. Begin with the given function:
[tex]\[
f(x) = 3^{x+2}
\][/tex]
2. To find the [tex]\( y \)[/tex]-intercept, set [tex]\( x = 0 \)[/tex]:
[tex]\[
f(0) = 3^{0+2}
\][/tex]
3. Simplify the exponent:
[tex]\[
f(0) = 3^2
\][/tex]
4. Calculate [tex]\( 3^2 \)[/tex]:
[tex]\[
3^2 = 9
\][/tex]
Therefore, the [tex]\( y \)[/tex]-intercept of the function [tex]\( f(x) = 3^{x+2} \)[/tex] is the point [tex]\((0, 9)\)[/tex].
