A polynomial function has a root of –7 with multiplicity 2, a root of –1 with multiplicity 1, a root of 2 with multiplicity 4, and a root of 4 with multiplicity 1. If the function has a positive leading coefficient and is of even degree, which statement about the graph is true?
The graph of the function is positive on (2, 4).
The graph of the function is negative on (4, mc026-1.jpg).
The graph of the function is positive on (mc026-2.jpg, –1).
The graph of the function is negative on (–7, –1).

Question

A polynomial function has a root of –7 with multiplicity 2, a root of –1 with multiplicity 1, a root of 2 with multiplicity 4, and a root of 4 with multiplicity 1. If the function has a positive leading coefficient and is of even degree, which statement about the graph is true?
The graph of the function is positive on (2, 4).
The graph of the function is negative on (4, mc026-1.jpg).
The graph of the function is positive on (mc026-2.jpg, –1).
The graph of the function is negative on (–7, –1).

anonymous · Answer

Positive leading coefficient and even degree means both ends of the graph go up|dw:1432599382025:dw|

anonymous · Answer

the graph will touch/bounce off |dw:1432599538223:dw|roots with even multiplicity, and cross roots with odd multiplicities