A polynomial function has a root of -5 with multiplicity 3, a root of 1 with multiplicity of 2, and a root of 3 with multiplicit
y 7.
If the function has a negative leading coefficient and is of even degree which statement about the graph is true?
a) function is positive on (-∞,-5)
b) fuction is negative on (-5,3)
c) function is positive on (-∞,1)
d) function is negative on (3,∞)
If the function has a negative leading coefficient and is of even degree which statement about the graph is true?
a) function is positive on (-∞,-5)
b) fuction is negative on (-5,3)
c) function is positive on (-∞,1)
d) function is negative on (3,∞)
2 answers:
Answer:
d) function is negative on (3,∞)
Step-by-step explanation:
The even degree and negative leading coefficient tell you that the function is negative as x ⇒ ±∞. (Selections A and C cannot be correct.)
The odd multiplicity tells you the function crosses the x-axis at x=-5 and x=3, so will be <em>non-negative</em> between those values. (Selection B cannot be correct.)
The function is negative on (3, ∞).
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