How does the graph of $$ f(x)=2^{x+2} $$ compare to the graph of $$ g(x)=2^{x}+2 $$ ? The graph of $$ f(x) $$ is a translation of the parent function $$ h(x)=2^{x} \square $$ unit(s) $$ \square $$ whereas the graph of $$ g(x) $$ is a translation of the parent function $$ h(x)=2^{x} $$ unit(s) (Type whole numbers.)

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The graph of $$ f(x) = 2^{x+2} $$ and $$ g(x) = 2^{x} + 2 $$ can be compared to the parent function $$ h(x) = 2^{x} $$ through translations.

1. **For $$ f(x) = 2^{x+2} $$:**
   - **Translation Type:** Horizontal shift
   - **Units:** 2 units to the **left**
   
   **Explanation:** The expression $$ x + 2 $$ inside the exponent indicates a shift to the left by 2 units. This is because adding a positive number inside the function argument moves the graph in the opposite direction on the x-axis.

2. **For $$ g(x) = 2^{x} + 2 $$:**
   - **Translation Type:** Vertical shift
   - **Units:** 2 units **up**
   
   **Explanation:** Adding 2 outside the exponent shifts the graph upward by 2 units. This affects all y-values, moving the entire graph higher on the y-axis.

**Summary:**
- **$$ f(x) = 2^{x+2} $$** is a translation of $$ h(x) = 2^{x} $$ **2 units to the left**.
- **$$ g(x) = 2^{x} + 2 $$** is a translation of $$ h(x) = 2^{x} $$ **2 units upward**.
The graph of $$ f(x) = 2^{x+2} $$ is a horizontal shift of the parent function $$ h(x) = 2^{x} $$ **2 units to the left**, while the graph of $$ g(x) = 2^{x} + 2 $$ is a vertical shift of $$ h(x) = 2^{x} $$ **2 units upward**.

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