Graph the function $$ f(x)=2^{x-2}+4 $$. Give the domain and range. Use the graphing tool to graph the function. The domain of the function $$ f(x)=2^{x-2}+4 $$ is $$ (-\infty, \infty) $$. (Type your answer in interval notation.) The range of the function $$ f(x)=2^{x-2}+4 $$ is (Type your answer in interval notation.)

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To analyze the function $$ f(x) = 2^{x-2} + 4 $$, we can determine its domain and range.

### Domain
The function $$ f(x) = 2^{x-2} + 4 $$ is defined for all real numbers $$ x $$ because the exponential function $$ 2^{x-2} $$ is defined for all $$ x $$. Therefore, the domain is:
$$
(-\infty, \infty)
$$

### Range
Next, we analyze the range of the function. The term $$ 2^{x-2} $$ is an exponential function that approaches 0 as $$ x $$ approaches negative infinity and increases without bound as $$ x $$ approaches positive infinity.

Thus, the minimum value of $$ 2^{x-2} $$ is 0 (as $$ x \to -\infty $$), and the maximum value is unbounded (as $$ x \to \infty $$).

Adding 4 to $$ 2^{x-2} $$ shifts the entire graph up by 4 units. Therefore, the minimum value of $$ f(x) $$ is:
$$
0 + 4 = 4
$$
And since $$ 2^{x-2} $$ can grow indefinitely, $$ f(x) $$ can also grow indefinitely. Thus, the range of $$ f(x) $$ is:
$$
[4, \infty)
$$

### Summary
- **Domain**: $$ (-\infty, \infty) $$
- **Range**: $$ [4, \infty) $$

You can graph the function using a graphing tool to visualize it. The graph will show an exponential curve that approaches the horizontal line $$ y = 4 $$ as $$ x $$ decreases and rises steeply as $$ x $$ increases.
- **Domain**: $$ (-\infty, \infty) $$ - **Range**: $$ [4, \infty) $$

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