Sketch the graph the following piecewise function fx 2 x le

Sketch the graph the following piecewise function. f(x) = {-2, x lessthanorequalto 0 9 - x^2, 0

Solution

1) f(-1)=3     draw a vertical line from 1 it meets at 3

2) Domain of f(x) is x belongs to [-2,2]

3) Range of f(x) is y belongs to [-1,3]

4) at x= 0 , f(x)=1  

5) In [-2,0]   f(x) >1

6) maximium at x=-1,2   at   x=-1 absolute maximum and at x =2 local maximim

     minimum at x=-2,1     at   x=-2 local minimum and at x=1 absolute minimum

7) function is inceasing in [-2,-1] ,[1,2]

    function is decreasing in [-1,1]