Let's solve the problem step by step, following the function definition [tex]\( g(x) = 2^{x+2} \)[/tex].
### Step-by-Step Solution
1. Identify the function: We are given a function [tex]\( g(x) = 2^{x+2} \)[/tex].
2. Evaluate the function at the given values of [tex]\( x \)[/tex]:
- For [tex]\( x = -2 \)[/tex]:
[tex]\[
g(-2) = 2^{(-2) + 2} = 2^0 = 1
\][/tex]
So, [tex]\( y = 1 \)[/tex].
- For [tex]\( x = -1 \)[/tex]:
[tex]\[
g(-1) = 2^{(-1) + 2} = 2^1 = 2
\][/tex]
So, [tex]\( y = 2 \)[/tex].
- For [tex]\( x = 0 \)[/tex]:
[tex]\[
g(0) = 2^{0 + 2} = 2^2 = 4
\][/tex]
So, [tex]\( y = 4 \)[/tex].
3. Summarize the results:
- [tex]\( g(-2) = 1 \)[/tex]
- [tex]\( g(-1) = 2 \)[/tex]
- [tex]\( g(0) = 4 \)[/tex]
These calculations give us the following table:
[tex]\[
\begin{array}{rl}
g(x) & =2^{x+2} \\
x & y \\
\hline
-2 & 1 \\
-1 & 2 \\
0 & 4
\end{array}
\][/tex]
Thus, the values of [tex]\( y \)[/tex] for [tex]\( x = -2, -1, \)[/tex] and [tex]\( 0 \)[/tex] are 1, 2, and 4 respectively.
