Answer :
To find the \( y \)-intercept of the function \( f(x) = 3^{x+2} \), we need to determine the value of the function when \( x = 0 \).
1. Set \( x = 0 \) in the function:
[tex]\[ f(0) = 3^{0+2} \][/tex]
2. Simplify the exponent:
[tex]\[ 0 + 2 = 2 \][/tex]
3. So the function simplifies to:
[tex]\[ f(0) = 3^2 \][/tex]
4. Calculate \( 3^2 \):
[tex]\[ 3^2 = 9 \][/tex]
Therefore, the \( y \)-intercept of the function \( f(x) = 3^{x+2} \) is the point where \( x = 0 \) and \( y = f(0) = 9 \). The coordinates of this point are \( (0, 9) \).
So, the correct answer is:
B. [tex]\( (0, 9) \)[/tex]
1. Set \( x = 0 \) in the function:
[tex]\[ f(0) = 3^{0+2} \][/tex]
2. Simplify the exponent:
[tex]\[ 0 + 2 = 2 \][/tex]
3. So the function simplifies to:
[tex]\[ f(0) = 3^2 \][/tex]
4. Calculate \( 3^2 \):
[tex]\[ 3^2 = 9 \][/tex]
Therefore, the \( y \)-intercept of the function \( f(x) = 3^{x+2} \) is the point where \( x = 0 \) and \( y = f(0) = 9 \). The coordinates of this point are \( (0, 9) \).
So, the correct answer is:
B. [tex]\( (0, 9) \)[/tex]
