Question

Guven the following absolute value function sketch the graph of yhe function and find the domain and range. F (x) = |x + 3| - 1

Answer 1

See below

Explanation:

The graph is formed from f(x) = |x|.

f(x) = |x| is shaped like a V with the vertex at the origin and the slope of each arm = 1. Then f(x) = |x + 3| will have the same shape but will be moved 3 units to the left so the vertex is at (-3,0). The - 1 ( to give f(x) = |x + 3| - 1) translates the whole graph 1 unit down so the vertex is at the point (-3, -1).

The domain is All Real x and the range = All real values of f(x)

equal or greater than -1.