Answered

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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 [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]
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