"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. 2.5 to 3.5
B. 3.5 to 4.5
C. 5.5 to 6.5
D. -2.5 to -1.5
E. -1.5 to -0.5
F. 1.5 to 2.5"

Its very simple.
Just look at the graph and see the points where the graph is intersecting the x-axis.Roots are the points where the graph crosses the x-axis.
Hence,
The graph is apparently crossing the x-axis at
x = -1
x = 2
x = 6
So,now it easy to define the domain of the function from the given options.

F. 1.5 to 2.5
C. 5.5 to 6.5

I hope it helped.

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"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. 2.5 to 3.5 B. 3.5 to 4.5 C. 5.5 to 6.5 D. -2.5 to -1.5 E. -1.5 to -0.5 F. 1.5 to 2.5"

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"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. 2.5 to 3.5
B. 3.5 to 4.5
C. 5.5 to 6.5
D. -2.5 to -1.5
E. -1.5 to -0.5
F. 1.5 to 2.5"