Graph the function $$ f(x)=6^{x}+2 $$. Give the domain and range. Use the graphing tool to graph the function. The domain of the function $$ f(x)=6^{x}+2 $$ is $$ (-\infty, \infty) $$. (Type your answer in interval notation.) The range of the function $$ f(x)=6^{x}+2 $$ is (Type your answer in interval notation.)

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To analyze the function $$ f(x) = 6^x + 2 $$, we can determine its domain and range.

### Domain:
The function $$ f(x) = 6^x + 2 $$ is defined for all real numbers $$ x $$ because the exponential function $$ 6^x $$ is defined for all $$ x $$. Therefore, the domain is:
$$
(-\infty, \infty)
$$

### Range:
The exponential function $$ 6^x $$ has a range of $$ (0, \infty) $$ since it approaches 0 as $$ x $$ approaches negative infinity and increases without bound as $$ x $$ approaches positive infinity.

When we add 2 to $$ 6^x $$, the entire function shifts up by 2. Thus, the minimum value of $$ f(x) $$ occurs as $$ x $$ approaches negative infinity, where $$ 6^x $$ approaches 0, making $$ f(x) $$ approach 2. The function increases without bound as $$ x $$ increases. Therefore, the range of $$ f(x) $$ is:
$$
(2, \infty)
$$

### Summary:
- **Domain**: $$ (-\infty, \infty) $$
- **Range**: $$ (2, \infty) $$

You can graph the function $$ f(x) = 6^x + 2 $$ using a graphing tool to visualize its behavior. The graph will show an exponential curve that approaches the horizontal line $$ y = 2 $$ as $$ x $$ goes to negative infinity and rises steeply as $$ x $$ increases.
- **Domain**: $$ (-\infty, \infty) $$ - **Range**: $$ (2, \infty) $$

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