Question

PLEASE HELP!!!!!!!!!!! The points plotted below are on the graph of a polynomial. In what range of x-values must the polynomial have a root? Check all that apply. A. x=-4.6 B.x=-3.5 C.-2.3 D.-0.21 E.1 F.3

Answer 1

ever heard of the intermediate value theorem?

Answer 2

@TaylorNeedsHelp no

Answer 3

Those aren't even complete answers. @cashmereonly polynomial functions are continuous like pieces of string; if you know one end of the string is on side of a piece of paper (our \(x\)-axis), and the other end is on the *other* side of the piece of paper, surely somewhere in the middle there it has to cross the paper, right?

Answer 4

In other words, a chicken (traveling along our function), to get from one side to the other, must cross the road... right? I suppose it's like "how did the chicken get to the other side?" -- well, by crossing the road! The road in our case is the \(x\)-axis.

Answer 5

So look at our plot. Everytime there is a point (our chicken) on one side of the \(x\)-axis (our road), and then a little while later (giving the chicken some time) the next point (our chicken) is on the *other* side, our function (his path) had to have crossed the \(x\)-axis. *Where* he crosses the road is what our roots are.

Answer 6

http://puu.sh/2Agso
Those red spots will be roughly where he crosses (we can't tell exactly where just by eye-balling it because his path is curved).