We are asked to graph the function `y=log_4(x+2)-1 ` :

This is a translation of the graph of ` y=log_4x ` 2units left and 1 unit down.

The domain is x>-2 and the range is all real numbers. There is a vertical asymptote at x=-2 and the function is increasing and concave down on its domain.

Some points on the graph: (-31/16,-3),(-7/4,-2),(-1,-1),(2,0),(14,1).

The graph: