What is the range of $$ \mathrm{f}(\mathrm{x})=3+3^{\mathrm{x}-2} $$ ? (Type your answer in interval notation.)

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To find the range of the function $$ f(x) = 3 + 3^{x-2} $$, we will analyze the behavior of the function as $$ x $$ varies.

1. **Identify the base function**: The term $$ 3^{x-2} $$ is an exponential function. Exponential functions have specific characteristics:
   - They are always positive for all real numbers $$ x $$.
   - As $$ x $$ approaches negative infinity, $$ 3^{x-2} $$ approaches 0.
   - As $$ x $$ approaches positive infinity, $$ 3^{x-2} $$ approaches positive infinity.

2. **Determine the minimum value**: The minimum value of $$ 3^{x-2} $$ occurs as $$ x $$ approaches negative infinity, where $$ 3^{x-2} $$ approaches 0. Therefore, the minimum value of $$ f(x) $$ is:
   $$
   f(x) \to 3 + 0 = 3
   $$

3. **Determine the maximum value**: As $$ x $$ approaches positive infinity, $$ 3^{x-2} $$ approaches positive infinity, which means:
   $$
   f(x) \to 3 + \infty = \infty
   $$

4. **Combine the results**: The function $$ f(x) $$ can take any value greater than or equal to 3.

Thus, the range of $$ f(x) = 3 + 3^{x-2} $$ in interval notation is:
$$
[3, \infty)
$$
The range of $$ f(x) = 3 + 3^{x-2} $$ is all real numbers greater than or equal to 3, which is written as $$[3, \infty)$$.

What is the range of ?
(Type your answer in interval notation.)

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What is the range of ? (Type your answer in interval notation.)