explain how the graph of f(x)=log2x transforms to g(x)=-log2(x+4)

Question

explain how the graph of f(x)=log2x transforms to g(x)=-log2(x+4) 

Answer 1

f(x) = log(2x)

 

g(x) = -log(2(x+4))

 

g(x) has two transforms from f(x), shown in orange. 

 

The first transform switches the sign from + log to - log.  This causes the graph to be reflected about the x-axis.

 

The second transform replaces x with (x+4).  Adding the 4 shifts the graph 4 places to the left along the x-axis.