F(x) is an even function with the domain -4 to 4 if f(x) is increasing for 0 to 2 and decreasing from 2 to 4 describe its behavior for all negative values of X

Question

We also need to list the local extrema of f(x), I know this means the oocal minimum or maximum.

Answer 1

f(x)=f(-x) for an even function. For x between -2 and 0 f(x) is decreasing, and for x between -4 and -2 it is increasing. 

The following piecewise function satisfies the requirements.

f(x)=

{ |x| for -2≤x≤2

{ 4-x for 2<x≤4

{ 4+x for -4≤x<-2

The extrema are maxima at x=-2 and x=2, minimum at x=0. You could include minima at x=-4 and x=4 for the given domain.