To identify the intervals on which the function $f(t)$ is increasing, we should look at where the graph moves upward as $t$ increases.

From examining the provided graph:

1. The function decreases from $t = -\infty$ to around $t = 1$.
2. It starts increasing from $t = 1$ to around $t = 3$.
3. The function decreases again between $t = 3$ and $t = 4$.
4. Finally, it increases from $t = 4$ onward.

Based on this observation, the correct intervals where the function appears to be increasing are:

• $(1, 3)$
• $[4, \infty)$

The best match from the answer choices would be:

• $(1, 3) \cup [4, \infty)$

Would you like further clarification on this solution, or do you have any other questions?

Here are some related questions to deepen your understanding:

1. What are the characteristics of an increasing interval in a function's graph?
2. How can we determine whether a function is increasing or decreasing using its derivative?
3. Why do open and closed intervals matter when describing where a function increases?
4. Can a function have multiple intervals where it increases or decreases?
5. How would this analysis change if we had a different type of function, like an exponential or logarithmic function?

Tip: In interval notation, use a closed bracket [ ] when the endpoint is included in the interval and an open bracket ( ) when it is not.