1. Problem 6 asks to find the increasing and decreasing intervals for a function with two vertical asymptotes between $x=-2$ and $x=2$. The graph approaches $+\infty$ to the left of the first asymptote, then drops to $-\infty$ between the asymptotes, and rises again to $+\infty$ to the right of the second asymptote. There is a U-shape between $x=-2$ and $x=2$. 2. From the graph description for problem 6, the function is increasing on the intervals $(-\infty,-2)$ and $(2,\infty)$ because it goes up to positive infinity at both ends outside the asymptotes. 3. The function is decreasing on the interval $(-2,2)$ because it drops from $+\infty$ down to $-\infty$ between the asymptotes. 4. Problem 7 asks to find the relative extrema points (minimum and maximum) and the increasing/decreasing intervals for a graph that looks like a double valley (double dip) inside a downward-opening curve from $x=-6$ to $x=6$. 5. The two relative minimum points are the bottoms of the dip, located approximately at their x-values where the graph dips below the x-axis. We label these approximate x-values as $x=a$ and $x=b$ where $-6 < a < b < 6$. 6. The relative maximum occurs roughly between these minima where the graph reaches a local peak. 7. The function increases on the intervals leading up to each relative minimum and after each relative minimum going toward the relative maximum or the ends. 8. The function decreases between the relative maximum and each relative minimum. Summary answers: - Problem 6: Increasing intervals: $(-\infty,-2) \cup (2,\infty)$ Decreasing interval: $(-2,2)$ - Problem 7: Relative minima at approximately $x=a$ and $x=b$ (exact values not given) Relative maximum between $a$ and $b$ Increasing intervals: $(-6,a)$ and $(b,6)$ Decreasing interval: $(a,b)$