Question

the degree of the polynomial function on the graph is between 3 and 6, inclusive. what is the polynomial? http://loncapa.tcc.fl.edu/cgi-bin/plot.png?file=murph99j_tccfl_1392254072_54582799_plot.data

Answer 1

Assuming we see all of this graph that is interesting...

3, 4, 5, 6

Starts down (large negative values of x) and end down (large positive values of x). Since these are the same direction, the degree MUST be even.

4, 6

There appear to be four zeros. No multiplicities. The degree must be 4

4

Both ending down suggests a negative leading coefficient.

Zeros of -4, -1, 0, 4 (assuming our eyes can be trusted) suggest, among other things, that the constant term is zero and the coefficient on the x-term is -16

Well, is that enough to solve the problem? We're just walking through it and seeing what we know. Nothing fancy.