The function provided is $f(x) = 2^x + 3$.

To find the domain of the function using graphing technology or by reasoning analytically:

Domain of $f(x) = 2^x + 3$:

• The base function here is $2^x$, which is an exponential function.
• Exponential functions like $2^x$ are defined for all real numbers, meaning $x$ can take any real value.
• Adding a constant (in this case, $+3$) does not affect the domain of the function.

Thus, the domain of $f(x) = 2^x + 3$ is:

$\boxed{(-\infty, \infty)}$

This means that the function is defined for all real numbers.

Would you like more details on graphing this function or any further clarification?

Here are some related questions to explore:

1. What is the range of the function $f(x) = 2^x + 3$?
2. How does the function behave as $x \to \infty$ and $x \to -\infty$?
3. How would you graph this function manually without technology?
4. What happens if the base of the exponential is changed, for example, to $f(x) = 3^x + 3$?
5. Can you describe any horizontal asymptotes of this function?

Tip: When dealing with exponential functions, the domain is almost always all real numbers, but be sure to check for any potential restrictions (like logarithmic terms or square roots in more complex cases).