The graph shown is of an exponential function $f(x)$. For exponential functions, the general form is $f(x) = a \cdot b^x$ where $a$ is a constant and $b$ is the base of the exponential. If $b > 1$, the function increases as $x$ increases; if $0 < b < 1$, the function decreases as $x$ increases.

From the graph, the function increases as $x$ increases and approaches infinity ($+\infty$), indicating $b > 1$. Additionally, as $x$ decreases and goes towards negative infinity ($-\infty$), the function approaches a horizontal asymptote, which looks like it is around $y = 3$.

Therefore, the correct option representing the end behavior of the function is:

• As $x \to -\infty$, $f(x) \to 3$
• As $x \to \infty$, $f(x) \to \infty$

This matches the fourth option in the given choices.

Would you like a detailed explanation or have any questions about this problem?

Here are 5 related questions to expand on this topic:

1. What is the general formula for exponential growth and decay?
2. How does the base $b$ of an exponential function affect its growth or decay?
3. What is an asymptote, and why do exponential functions often have them?
4. How can you determine the horizontal asymptote of an exponential function from its equation?
5. How do transformations like shifting or stretching affect the graph of an exponential function?

Tip: When analyzing the end behavior of functions, always look for horizontal asymptotes and consider how the function behaves as $x$ approaches both positive and negative infinity.