The horizontal asymptote of the function $y = 2^x + b$ is determined by analyzing the behavior of the function as $x$ approaches infinity or negative infinity.

• As $x$ approaches infinity ($x \to \infty$), $2^x$ grows exponentially large, so $y = 2^x + b$ also grows without bound, meaning there is no horizontal asymptote in this direction.

• As $x$ approaches negative infinity ($x \to -\infty$), $2^x$ approaches 0. Therefore, $y = 2^x + b$ approaches $y = 0 + b = b$.

Thus, the horizontal asymptote of the function $y = 2^x + b$ is $y = b$.

Would you like more details or have any questions?

Here are 5 related questions:

1. How do you find vertical asymptotes in other types of functions?
2. What is the general form of a function with an exponential component?
3. How does changing the base of the exponential function affect its graph?
4. What happens to the horizontal asymptote if a coefficient is added to $2^x$ instead of a constant?
5. Can a function have more than one horizontal asymptote?

Tip: Horizontal asymptotes describe the end behavior of a function, indicating what value $y$ approaches as $x$ goes to infinity or negative infinity.