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What is the [tex]$y$[/tex]-intercept of [tex]$f(x) = 3^{x+2}$[/tex]?

A. [tex]$(9,0)$[/tex]
B. [tex]$(0,9)$[/tex]
C. [tex]$(0,-9)$[/tex]
D. [tex]$(9,-9)$[/tex]

Sagot :

GinnyAnswer
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]
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