Subjects algebra

Function Behavior 7B5627

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1. **State the problem:** We are given a function representing distance traveled over time during a kayak trip. We need to determine which statement about the function is true: whether it is never constant, always increasing, or never decreasing. 2. **Understand the function behavior:** The graph shows distance vs. time. The line increases, then flattens (constant), then increases again. 3. **Recall definitions:** - A function is **constant** if its value does not change over an interval. - A function is **increasing** if for any two times $t_1 < t_2$, $f(t_1) < f(t_2)$. - A function is **decreasing** if for any two times $t_1 < t_2$, $f(t_1) > f(t_2)$. 4. **Analyze the graph:** - The function is not always increasing because it flattens (constant) for some time. - The function is never decreasing because the distance never goes down. - The function is sometimes constant (flattened part), so it is not never constant. 5. **Conclusion:** The true statement is: **The function is never decreasing**. Final answer: The function is never decreasing.