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?
A. The graph of the function is positive on (2, 4).
B. The graph of the function is negative on (4,infinity).
C. The graph of the function is positive on (-infinity, –7).
D. The graph of the function is negative on (–7, –1).

Answer 1

Answer:

Step-by-step explanation:

From the information given in the problem, our function will be

where  is a positive leading coefficient.

Now, we just need to go through the answer choices and plug in x values that are in each interval.

A) 3 is between (2,4) so let's test  

is not a positive number, so A is wrong

B)  

is not a negative number, so B is also wrong.

C)  

is a positive number, so C is correct.

D) Just to make sure, let's check D.

is not a negative number, so D is also wrong.

Answer 2

Answer:

Step-by-step explanation:

c