Question

What is the range of the function f(x) = |x| – 3?

Answer 1

Why not draw the graph of y=|x|?  It has a v-shape, and the vertex is at (0,0).

The graph of f(x) = |x| - 3 looks exactly the same, EXCEPT that the whole graph of |x| is shifted 3 units downward.  The smallest value that y can have is therefore -3.

Can you now figure out the range of f(x)?