1.) Where is the function, f(x), increasing? Where is it decreasing? How can you tell from this graph? Explain.
on this graph the F(x) is increasing between (-2, 0) U (0, 2) tha is because on this interval is the only time that f'(x) produces positive outputs and not outputs that are equal zero or negative numbers.

2.)Where is there an extrema?
Well on this graph it seems that there are three extrema points. One piont is at F'(0) that is because at that pointis when f'(x) is equal to zero alos there is a change of signs there from being negative to positive so this would be a local minimun. the other two extremas would be when f'(x) is equal to both + and - 1. 25 at these points there are both local maximums.

Where is the function, f(x), concave up? Where is it concave down? How can you tell from this graph?
on this graph it concaves up between (-∞, -1.25) U (0, 1.25) because in this interval is the only time the derivative of this graph would be positive and it also be f''(x) which would make it true.
between (-1.25, 0)U(1.25, ∞) is where is concaves down. on that interval the f'(x) makes anegative slope so then on the double prime graph there would be a negative value on the double prime

Sketch the graph f(x) on a sheet of paper. Which power function could it be? Explain your reasoning.
well it seems that the power graph is x to the fifth by the way the graphs are turning up. Because the f''(x) looks like a graph of x to the thrid power so then the original graph would have the parent fuction is x to the fifth.