the polynomial function ( f ) is an odd function with domain ( -4leq xleq4 ). the table gives information…
the polynomial function ( f ) is an odd function with domain ( -4leq xleq4 ). the table gives information about values of ( f(x) ) and the behavior of the function.\nwhat is the absolute maximum value of ( f ) on its domain?
Answer
Explanation:
Step1: Recall the property of odd function
An odd function satisfies (f(-x)=-f(x)). The domain is (-4\leq x\leq4). We can use the symmetry of the odd - function.
Step2: Analyze the given values
We know the values for (0 < x\leq4). For an odd function, if (x) is in the domain, then (-x) is also in the domain. When (x = 4), (f(4)=2). When (x=- 4), by the property of odd function (f(-4)=-f(4)=- 2). When (x = 3), (f(3)=0). When (x=-3), (f(-3)=-f(3)=0). When (x = 2), (f(2)=-3). When (x=-2), (f(-2)=-f(2)=3). When (x = 1), (f(1)=-1). When (x=-1), (f(-1)=-f(1)=1).
Step3: Determine the absolute maximum
The absolute maximum value of a function (y = f(x)) on an interval ([a,b]) is the largest value of (y) in that interval. We check all the values: (f(-4)=-2), (f(-3)=0), (f(-2)=3), (f(-1)=1), (f(0)=0), (f(1)=-1), (f(2)=-3), (f(3)=0), (f(4)=2)
Answer:
(3) (corresponding to option B)