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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.

Given the function f(t) in the graph below, identify the intervals on which the function appears to be increasing.

Learn how to identify the intervals where a function is increasing by analyzing its graph. This problem involves understanding the behavior of functions on intervals and applying concepts of increasing and decreasing intervals, ideal for students in Grades 10-12.

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