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, infinity).
The graph of the function is positive on (negative infinity, –7).
The graph of the function is negative on (–7, –1).

Answer 1

Answer:

• C. The graph of the function is positive on (negative infinity, –7).

Step-by-step explanation:

With given conditions we can state:

• The graph is positive between (-∞, -7)∪(-7, -1)∪(4, +∞), since it touches -7 and is positive either side of it.
• The graph is negative between (-1, 2) and (2, 4), since it touches 2 and is negative either side of it.
• Overall shape is U as leading coefficient is positive and is of even degree.

Comparing with the answer choices, correct choice is C.