graph f(x)=|x|-1

Question

find the interval of f(x)=|x|-1 and graph

Answer 1

The vertex of the graph will be at (0, -1), not (0, 1).

 

 

It will be a giant V with the vertex of the V at (0, -1).

 

The slope of the left side of the V is -1, and the slope of the right side of the V is 1.

 

 

Other points would be (1, 0), and (-1, 0), (2, 1) and (-2, 1).

 

 

 

Answer 2

f(x ) = l X l - 1

 

 Theory of graph:  Given graph of  f (x ) , then the graph of  f( X) - 1 will be graph of f(x) shifted vertically 1 unit.

   So here 

 

      f(x) +1 = l X l  will be lXl shift up 1 unit.

 

         so will be from point ( 0, 1) 2 lines of 45 degree and - 45 degree.