Let f(x) be the piecewise

Question

Let y=f(x) be the piecewise defined function given below.
f(x)=⎧⎩⎨⎪⎪−x−1,0,x−1, if x≤−1, if −1<x<1, if x≥1.
a. f(−2)=
help (numbers)

b. f(1)=
0
help (numbers)

c. For what values of x is f(x)=0?


-
help (inequalities)

d. Find the domain and range of f. (You may find it helpful to graph this function on your own paper to find the domain and range.) Your answers must be inequalities (not intervals 

 

Domain:
Range:

Answer 1

         -x-1, if x ≤ -1

 

f(x) =    0, if -1 < x < 1

 

          x - 1, if x ≥ 1

 

Since -2 < -1, f(-2) = -(-2)-1 = 1

 

Since 1 ≥ 1, f(1) = 1-1 = 0

 

Domain = set of all possible values of x

 

            = -∞ < x < ∞  (the set of all real numbers)

 

Range = set of all possible values of y

 

          = 0 ≤ y < ∞